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

generates a code of length 53 over Z3[X]/(X^2) who´s minimum homogenous weight is 100.

Homogenous weight enumerator: w(x)=1x^0+108x^100+94x^102+108x^103+100x^105+26x^108+216x^109+54x^112+14x^129+8x^132

The gray image is a linear code over GF(3) with n=159, k=6 and d=100.
This code was found by Heurico 1.16 in 0.572 seconds.