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

generates a code of length 27 over Z5[X]/(X^2) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+188x^90+440x^95+348x^100+2500x^104+496x^105+10000x^109+548x^110+472x^115+400x^120+176x^125+44x^130+12x^135

The gray image is a linear code over GF(5) with n=135, k=6 and d=90.
This code was found by Heurico 1.16 in 0.356 seconds.