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 1 1 1 1 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 2 X+1 X+2 0 1 X X X 2X+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 0 0 X X 0 0 2X X X X 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 X X 0 X X 0 X X 2X 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 0 2X 2X X 2X X X 0 0 X
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 2X 2X 2X X 0 2X 0 X X 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 0 X 0 X X X X 2X 2X 0 X
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 0 X X X 0 2X 2X X 0 X
generates a code of length 38 over Z3[X]/(X^2) who´s minimum homogenous weight is 57.
Homogenous weight enumerator: w(x)=1x^0+100x^57+18x^59+240x^60+168x^62+370x^63+156x^64+522x^65+486x^66+600x^67+1638x^68+598x^69+2574x^70+3600x^71+776x^72+5232x^73+5760x^74+732x^75+8286x^76+6390x^77+844x^78+6336x^79+4932x^80+822x^81+2712x^82+2466x^83+696x^84+348x^85+702x^86+436x^87+48x^89+252x^90+142x^93+42x^96+20x^99+4x^102
The gray image is a linear code over GF(3) with n=114, k=10 and d=57.
This code was found by Heurico 1.16 in 25.3 seconds.