The generator matrix

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

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+1620x^100+240x^101+640x^102+520x^103+2260x^105+720x^106+1120x^107+460x^108+3412x^110+1040x^111+1240x^112+520x^113+1804x^115+16x^120+12x^125

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 786 seconds.