The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X X 1 1 X 1 1 1 1 1 1
0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 2X 2X X 2X 2X 2X X X 2X X 2X 0 2X X 2X X 0 X 2X 2X 0 0 2X 0 2X X 2X 2X 0 2X 2X X X 0 2X 0 X X 2X 0 X 2X X X X 0 X 0 0 X 0 X X 0
0 0 X 0 0 0 0 0 0 0 0 X 2X 2X 2X 2X 0 X 0 X X 2X X 2X 0 X 2X 0 2X 0 X X 0 2X 2X X 2X X 2X X X 2X 0 X 2X 0 X X 2X 0 2X 0 0 0 X 2X 2X 2X 2X X 2X X X 2X X 0 X 0 0
0 0 0 X 0 0 0 0 X 2X 2X 2X 0 0 X 0 X 2X X 2X 2X 2X 2X 0 0 0 2X 2X 0 X X X X 2X X 2X X X 2X X 0 X 0 0 2X 2X 2X 2X 2X 0 0 0 0 2X X 0 2X 2X X 0 2X 0 2X 0 X X 0 2X X
0 0 0 0 X 0 0 X 2X 0 2X 0 0 2X 2X X X X 2X X 0 2X X 2X X 0 X 2X 0 X 0 0 0 2X X 2X X X X 2X X X 0 2X X X X 2X 2X 0 2X 2X X X X X X 0 2X 2X 2X 2X 2X X 0 0 0 X X
0 0 0 0 0 X 0 2X 2X X 0 2X 2X 2X 2X 2X 2X 0 X 0 0 2X 2X 0 2X X 2X 0 0 X 2X X 2X X 2X 2X 2X 2X 2X 0 X X 0 2X X 0 0 0 X X 0 0 X 0 0 2X 2X 0 0 0 0 0 X 0 X 2X 2X 0 2X
0 0 0 0 0 0 X 2X 2X 2X 2X 2X 2X X X X 0 2X 0 0 X 0 2X 2X 2X 0 X X 0 X 0 0 2X X 0 X 0 2X 0 2X 0 0 X 0 X X 0 X 2X 0 2X 0 2X 2X X 2X 2X 0 0 0 0 2X 2X 2X X 2X 0 0 X
generates a code of length 69 over Z3[X]/(X^2) who´s minimum homogenous weight is 120.
Homogenous weight enumerator: w(x)=1x^0+70x^120+174x^123+208x^126+234x^129+54x^130+204x^132+432x^133+186x^135+1296x^136+172x^138+1728x^139+184x^141+864x^142+178x^144+142x^147+120x^150+122x^153+70x^156+62x^159+32x^162+12x^165+8x^168+2x^171+2x^174+2x^177+2x^195
The gray image is a linear code over GF(3) with n=207, k=8 and d=120.
This code was found by Heurico 1.16 in 1.41 seconds.