The generator matrix

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

generates a code of length 51 over Z3[X]/(X^2) who´s minimum homogenous weight is 97.

Homogenous weight enumerator: w(x)=1x^0+42x^97+66x^98+236x^99+36x^100+42x^101+36x^102+48x^103+18x^105+12x^106+42x^107+110x^108+18x^109+12x^110+6x^112+4x^126

The gray image is a linear code over GF(3) with n=153, k=6 and d=97.
This code was found by Heurico 1.16 in 0.0303 seconds.