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.