The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1 3X  1  1  X  1  1  1  1  1  1  1  1  1
 0  1  0 3X  1 3X+1  3  X 2X+1 X+3 3X+2  2 4X+2 3X+3  1 2X+3 4X  1 2X+2 3X+3 X+2  X 4X 2X+4 2X+2 4X+3 4X+4
 0  0  1 3X+1  1 3X 2X+3 3X+3 4X+3 4X+2 4X+1 4X 4X+4 2X+4 2X+1 2X 3X+1 4X+3 X+1  2 2X+2  X  1 2X X+3 2X+3 4X+3

generates a code of length 27 over Z5[X]/(X^2) who´s minimum homogenous weight is 100.

Homogenous weight enumerator: w(x)=1x^0+1376x^100+360x^101+1000x^102+320x^103+1940x^105+1080x^106+1600x^107+360x^108+1968x^110+1560x^111+1900x^112+320x^113+1816x^115+24x^120

The gray image is a linear code over GF(5) with n=135, k=6 and d=100.
This code was found by Heurico 1.16 in 31.5 seconds.