The generator matrix
1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 X 1 1 1 X 2X 1 1 1 1 1 1 X 1 1
0 1 1 2 0 1 2 1 2X+1 1 0 2 X+2 2X+1 0 1 X 1 2 2 0 2X+1 2X 1 2X+1 X+1 0 1 1 X+2 2X+2 2X+2 2X+2 2X+2 X 1 0 0
0 0 2X 0 0 0 0 0 0 0 2X X X 2X 2X 0 2X X X 2X X 2X X 2X 2X 2X X 0 2X X 0 2X X X 2X X 0 0
0 0 0 X 0 0 0 X 2X X 0 2X X 2X 0 2X 0 X 0 2X X 0 2X 2X 2X 0 X X X X 2X X 2X 0 2X 0 0 0
0 0 0 0 X 0 X X X X X 2X 0 X 0 X 2X 2X 0 0 2X 2X 2X 0 2X 0 2X 0 0 2X 2X 2X 2X X 2X X 0 X
0 0 0 0 0 2X 2X 0 2X X 0 2X X X 2X X 2X 0 X X 2X X X 0 0 X 0 2X 2X X X 0 0 X X 0 2X 2X
generates a code of length 38 over Z3[X]/(X^2) who´s minimum homogenous weight is 63.
Homogenous weight enumerator: w(x)=1x^0+26x^63+214x^66+72x^67+90x^68+370x^69+144x^70+144x^71+560x^72+306x^73+414x^74+776x^75+378x^76+396x^77+756x^78+342x^79+342x^80+580x^81+180x^82+72x^83+200x^84+36x^85+90x^87+30x^90+34x^93+8x^96
The gray image is a linear code over GF(3) with n=114, k=8 and d=63.
This code was found by Heurico 1.16 in 0.364 seconds.