The generator matrix

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

generates a code of length 31 over Z5[X]/(X^2) who´s minimum homogenous weight is 110.

Homogenous weight enumerator: w(x)=1x^0+136x^110+920x^114+296x^115+2240x^119+652x^120+5260x^124+1240x^125+4080x^129+684x^130+28x^135+48x^140+32x^145+8x^150

The gray image is a linear code over GF(5) with n=155, k=6 and d=110.
This code was found by Heurico 1.16 in 0.199 seconds.