The generator matrix
1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 X 1 1 1 0 1 X 1 1 1 0 1 1 1 1 1 1 1 1 1 1 X 1 1 1
0 1 1 2 0 1 2 1 2X+1 1 0 2 X+2 2X+1 0 1 1 0 2 2 1 2X+1 1 X 2X+1 X+1 1 X 2X 2 X+2 X+2 2X+2 2 2X+1 2 X+2 X 0 X+1 0
0 0 2X 0 0 0 0 0 0 0 2X X X 2X 2X 2X 2X 2X 2X X X X 2X X X X 2X X X 0 X X 2X 2X 2X 2X 0 0 0 0 0
0 0 0 X 0 0 0 X 2X X 0 2X X 2X 2X 0 2X X 0 2X X 2X 0 X 0 0 X 2X 2X 2X 0 2X 2X 0 X 2X 0 0 2X X 0
0 0 0 0 X 0 X X X X X 2X 0 X X 0 2X 2X 0 0 2X 2X 2X 0 2X 0 2X 0 0 X X X 2X X X 0 0 0 0 0 X
0 0 0 0 0 2X 2X 0 2X X 0 2X X X 2X 2X X 2X 2X 0 2X X X 0 2X 2X 2X 2X X X 0 0 X 2X 2X 2X 2X X 0 2X 2X
generates a code of length 41 over Z3[X]/(X^2) who´s minimum homogenous weight is 69.
Homogenous weight enumerator: w(x)=1x^0+34x^69+24x^71+208x^72+54x^73+102x^74+466x^75+216x^76+210x^77+536x^78+216x^79+270x^80+676x^81+378x^82+420x^83+710x^84+432x^85+276x^86+626x^87+108x^88+138x^89+194x^90+54x^91+18x^92+110x^93+40x^96+28x^99+10x^102+6x^105
The gray image is a linear code over GF(3) with n=123, k=8 and d=69.
This code was found by Heurico 1.16 in 0.401 seconds.