The generator matrix

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

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+384x^110+460x^111+280x^112+1420x^114+3276x^115+3240x^116+860x^117+3740x^119+6752x^120+5420x^121+1340x^122+8260x^124+12100x^125+9100x^126+1620x^127+6580x^129+7984x^130+4280x^131+900x^132+60x^135+28x^140+32x^145+8x^150

The gray image is a linear code over GF(5) with n=155, k=7 and d=110.
This code was found by Heurico 1.16 in 4 seconds.