The generator matrix
1 0 0 1 1 1 1 1 0 2X 1 1 1 1 0 1 0 1 1 1 1 0 1 1 1 2X 1 1 1 X X 0 1 1 1 2X 0 1 0 2X 1 X
0 1 0 1 0 2 1 2 1 1 0 2X+1 2X+2 2 0 X 1 2X+1 2 0 2X 1 2X+2 X+1 X 1 X+2 2X+1 X 1 1 1 2X+1 2 2X+2 1 0 X+1 2X 1 1 1
0 0 1 2 1 2 1 0 2 2X+1 2 2X 2X+1 X 1 2X+2 X+2 X+2 2 X X+1 0 1 2X+1 1 X+1 1 X 2 0 X+1 2X+2 2X 2X+2 2X 0 1 2X+1 1 1 X+2 2X+2
0 0 0 2X 0 0 0 0 0 0 0 0 0 X X X 2X X X 2X X 2X X 0 2X X 2X 2X 0 0 X X X 0 X 2X X X X 2X X 0
0 0 0 0 2X 0 0 0 0 0 X 2X 2X 0 X 2X 2X X 0 0 2X X X 0 X 2X 0 2X 2X X X 0 0 0 2X 2X X 2X 0 2X 0 2X
0 0 0 0 0 X 0 X X 2X 2X 2X 2X 0 X X 2X X 2X 0 X 2X 0 X 2X X X X X 0 0 2X 0 0 2X 2X X 0 2X 2X X 2X
0 0 0 0 0 0 X X X X X 2X X X 0 0 X 2X 2X 2X X 2X 2X 0 X X 2X 0 0 2X X 0 0 0 2X 2X X 2X 0 X X 0
generates a code of length 42 over Z3[X]/(X^2) who´s minimum homogenous weight is 69.
Homogenous weight enumerator: w(x)=1x^0+158x^69+276x^70+484x^72+1260x^73+1210x^75+2898x^76+2010x^78+5256x^79+3452x^81+7776x^82+4488x^84+8982x^85+3978x^87+7380x^88+2530x^90+3924x^91+944x^93+1404x^94+262x^96+210x^97+90x^99+52x^102+18x^105+4x^108+2x^111
The gray image is a linear code over GF(3) with n=126, k=10 and d=69.
This code was found by Heurico 1.16 in 57.1 seconds.