The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  0 2X  1  1  1  0 2X  1  1  1  1  1 2X  1  1  1 2X  1  1  1  1  1 2X  1  1  1
 0  1  0  0  X 2X+1 2X+1  1 2X+2  2  2  1  0  X X+1 X+1  1  1  1 2X+2 2X+2 X+2 X+2  1 2X  0 2X+2  1 2X 2X 2X  0  X  1  2  2 X+1
 0  0  1  1 2X+2 2X X+2 X+1 2X+1  2  0  0  1 2X+2 2X  1 2X+1  2  2 2X+1  X  0  2 2X+2 X+1  X 2X+2 2X+1 X+2 2X+2  2  0 2X X+2 2X+1 X+2 2X
 0  0  0 2X 2X  0 2X 2X  X  X 2X 2X  X  X  X  0  X  0  X  0  X  0 2X  X  X 2X  0 2X  0  X  0  X  0  0 2X  0 2X

generates a code of length 37 over Z3[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+264x^68+228x^69+402x^71+174x^72+282x^74+80x^75+192x^77+138x^78+228x^80+68x^81+78x^83+26x^84+12x^86+12x^87+2x^93

The gray image is a linear code over GF(3) with n=111, k=7 and d=68.
This code was found by Heurico 1.13 in 89.7 seconds.