The generator matrix

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

generates a code of length 27 over Z5[X]/(X^2) who´s minimum homogenous weight is 91.

Homogenous weight enumerator: w(x)=1x^0+380x^91+60x^92+380x^93+1000x^94+2560x^95+4060x^96+1780x^97+4300x^98+4740x^99+10152x^100+12120x^101+8700x^102+13820x^103+13780x^104+27208x^105+30680x^106+25020x^107+30440x^108+26220x^109+45916x^110+40140x^111+24440x^112+23560x^113+14260x^114+14676x^115+10120x^116+56x^120+48x^125+8x^130

The gray image is a linear code over GF(5) with n=135, k=8 and d=91.
This code was found by Heurico 1.16 in 78.6 seconds.