The generator matrix

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

generates a code of length 31 over Z5[X]/(X^2) who´s minimum homogenous weight is 115.

Homogenous weight enumerator: w(x)=1x^0+684x^115+660x^116+100x^117+360x^118+1000x^119+1996x^120+1680x^121+220x^122+480x^123+500x^124+1892x^125+960x^126+60x^127+660x^128+1000x^129+2040x^130+1200x^131+120x^132+12x^135

The gray image is a linear code over GF(5) with n=155, k=6 and d=115.
This code was found by Heurico 1.16 in 0.158 seconds.