The generator matrix

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

generates a code of length 31 over Z5[X]/(X^2) who´s minimum homogenous weight is 116.

Homogenous weight enumerator: w(x)=1x^0+40x^116+240x^118+400x^119+320x^120+260x^121+320x^123+200x^124+100x^125+60x^126+440x^128+400x^129+192x^130+140x^131+8x^135+4x^140

The gray image is a linear code over GF(5) with n=155, k=5 and d=116.
This code was found by Heurico 1.16 in 0.0111 seconds.