The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 0 1 1 1 1 X 1 1 1 1 2X 1 1 2X 1 1 1 X 0 1 1 X 1 1 1 1 1 0 1 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 2X 1 1 1 1 1 1 1 1 1 X 1 1 X 1 0 X 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2X+1 2 1 0 2 2X+1 1 X 2 2X+1 1 1 2 0 2X+1 1 2X+1 0 X+2 0 1 X+1 2 X X+2 1 X+2 2X+1 1 X 2X+1 X+2 1 1 2 2X 1 2X X+2 2X+1 2X+2 X+1 1 0 X+2 1 0 1 X X+2 2X 1 2X+2 2X+2 X+2 0 0 2X 2X+2 2 X+1 X+2 0 X 2X 1 2 1 2 2X+1 2X+2 X 2 2X+2 0 1 2X+2 1 0 X 2X X 1 X 0 0
0 0 2X 0 0 0 0 0 0 2X X X X X 0 0 2X X 0 2X X 0 0 X X 2X 2X 0 0 2X 2X 2X 2X X 2X X X X 0 2X 2X X X 0 2X X 0 X X X 0 0 X 0 X 0 0 0 0 2X X 0 X 0 X 2X 2X 0 X X 2X X X 2X X X 2X X 0 0 0 X 0 X 2X 2X X 0 2X X 2X X 2X X 2X X X 0 0
0 0 0 X 0 0 0 0 0 0 0 2X 0 2X X 2X 0 2X X X 0 X 2X 2X X 0 2X 0 X 0 0 X X 2X 0 X X 2X 2X 2X 2X 0 X 0 2X 2X 2X 2X 2X X 0 2X 0 X 0 X 2X X 0 2X X X 0 X X X 2X X X X 2X X 0 2X 2X 0 2X 2X X X 2X X 2X 2X 2X 0 X X 2X X 2X 2X X 2X 2X 0 0 0 0
0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X 2X 2X X 2X 2X 2X X 2X 0 0 X X 0 X X X 0 0 2X 0 0 2X 2X X 0 2X X X X 0 X X 2X X 2X X 0 X 2X X 2X X X 2X 2X X 2X 0 0 0 X 2X X 0 X X 2X X 0 X 0 X 0 0 2X 2X X X 0 2X 2X X 2X 0 X 0 X 2X X 2X 2X 2X 0
0 0 0 0 0 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X 2X X 2X X 2X X 2X 2X X 2X 2X 2X X 2X 2X X X X X 2X X 2X X X 2X 2X X 2X 0 0 0 2X X X 2X X X 0 0 2X 0 2X X 2X 0 X X X 0 2X X 2X X 2X 0 X X X 0 0 2X X 0 X 0 0 0 2X 2X X 0 2X 0
0 0 0 0 0 0 X 0 2X 2X X 2X 0 2X 2X X 0 X 0 X 2X X X 2X 0 X X X X 0 X X 2X 2X 0 2X 0 X 2X 2X 0 0 0 2X 0 X 2X 2X X 2X X X X X 0 X X 2X X 2X 2X 2X 2X X 2X X 2X X 2X 0 0 2X 2X X X X 0 0 2X X 2X 0 0 0 X X 0 X X 2X X 0 X 2X 2X 2X 2X 0 0
0 0 0 0 0 0 0 X X 2X 0 2X 2X X X 0 0 0 0 2X 2X 0 2X 0 X 2X X X X X X 2X 2X 0 0 2X 2X 0 X 0 2X 2X 0 2X 0 X 0 X 2X 2X 0 2X 0 0 0 X 2X 0 2X X 2X X 0 X X 0 X X X 0 X 2X 2X X 2X 0 0 2X 0 X 0 0 2X 2X 0 2X 2X X 2X 2X 0 2X X X 2X X 0 2X 0
generates a code of length 99 over Z3[X]/(X^2) who´s minimum homogenous weight is 171.
Homogenous weight enumerator: w(x)=1x^0+40x^171+18x^173+134x^174+6x^175+60x^176+306x^177+168x^178+174x^179+392x^180+348x^181+480x^182+424x^183+738x^184+858x^185+432x^186+1404x^187+1758x^188+514x^189+2214x^190+2526x^191+518x^192+3162x^193+3534x^194+414x^195+3954x^196+4170x^197+412x^198+4530x^199+4218x^200+480x^201+3822x^202+3438x^203+428x^204+2706x^205+2556x^206+442x^207+1860x^208+1446x^209+390x^210+840x^211+678x^212+342x^213+354x^214+252x^215+276x^216+120x^217+48x^218+238x^219+18x^220+18x^221+138x^222+88x^225+12x^227+64x^228+46x^231+18x^234+20x^237+4x^243
The gray image is a linear code over GF(3) with n=297, k=10 and d=171.
This code was found by Heurico 1.16 in 96.7 seconds.