The generator matrix

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

generates a code of length 31 over Z5[X]/(X^2) who´s minimum homogenous weight is 107.

Homogenous weight enumerator: w(x)=1x^0+720x^107+840x^108+260x^109+776x^110+3460x^111+4360x^112+3400x^113+2740x^114+5848x^115+10460x^116+14600x^117+11540x^118+8220x^119+14160x^120+25760x^121+34040x^122+25980x^123+21800x^124+27012x^125+39760x^126+43080x^127+26120x^128+14480x^129+15192x^130+18060x^131+13200x^132+4620x^133+60x^135+48x^140+16x^145+8x^150+4x^155

The gray image is a linear code over GF(5) with n=155, k=8 and d=107.
This code was found by Heurico 1.16 in 93.8 seconds.