The generator matrix

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

generates a code of length 34 over Z3[X]/(X^2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+56x^57+114x^60+124x^63+102x^66+1458x^68+86x^69+58x^72+46x^75+62x^78+60x^81+10x^84+8x^87+2x^102

The gray image is a linear code over GF(3) with n=102, k=7 and d=57.
This code was found by Heurico 1.16 in 0.0652 seconds.