The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 X 0 1 1 0 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2 2X+1 1 1 X+2 0 2X+1 2 2X+1 1 0 2 2X+1 X 2X+1 2 X+1 0 X 1 1 2X 1 1 2X 0 1 0 0
0 0 2X 0 0 0 0 0 0 2X X 2X 2X 2X 2X 0 2X 0 X 2X X 0 2X 0 2X 2X X X 0 X X X X 2X X 2X 2X X 0 0 0 0
0 0 0 X 0 0 0 0 0 0 0 0 0 0 2X X 2X X 0 X 0 2X 2X X 2X X X 0 2X 2X X 0 2X 0 X 2X 2X 2X 0 X X 0
0 0 0 0 X 0 0 0 0 0 0 0 0 0 2X 2X X 0 2X X 2X X 0 X X X 0 2X X 2X 0 X X X 0 2X X 0 2X 2X 0 0
0 0 0 0 0 2X 0 0 X 2X 2X X 2X 0 2X 2X 2X X X 0 0 2X 2X 0 2X 0 2X 0 0 2X 0 0 X 0 2X X 2X 0 X 0 2X 0
0 0 0 0 0 0 X 0 X 0 X X X 2X 2X 0 X 2X 2X 0 2X X 2X 0 0 2X 0 X 0 2X 0 X 0 X X 2X 0 2X 0 X 2X 0
0 0 0 0 0 0 0 X X X X 0 2X X 2X X X X 0 2X 0 X 0 0 0 X 2X 0 X 2X 2X 2X X X 2X 0 0 X 2X X 2X 0
generates a code of length 42 over Z3[X]/(X^2) who´s minimum homogenous weight is 63.
Homogenous weight enumerator: w(x)=1x^0+46x^63+6x^65+178x^66+96x^68+328x^69+78x^70+276x^71+434x^72+474x^73+792x^74+554x^75+1500x^76+2178x^77+630x^78+3462x^79+4266x^80+656x^81+6018x^82+6228x^83+776x^84+6990x^85+6102x^86+734x^87+4884x^88+4140x^89+736x^90+2418x^91+1722x^92+562x^93+420x^94+372x^95+460x^96+66x^98+252x^99+138x^102+62x^105+8x^108+6x^111
The gray image is a linear code over GF(3) with n=126, k=10 and d=63.
This code was found by Heurico 1.16 in 29 seconds.