The generator matrix

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

generates a code of length 32 over Z5[X]/(X^2) who´s minimum homogenous weight is 111.

Homogenous weight enumerator: w(x)=1x^0+720x^111+840x^112+260x^113+1060x^114+2532x^115+5920x^116+3980x^117+2880x^118+6660x^119+8300x^120+16260x^121+9440x^122+8800x^123+16160x^124+24420x^125+36700x^126+19800x^127+20220x^128+30460x^129+39712x^130+46540x^131+19960x^132+15340x^133+18160x^134+13056x^135+16360x^136+5980x^137+24x^140+36x^145+40x^150+4x^155

The gray image is a linear code over GF(5) with n=160, k=8 and d=111.
This code was found by Heurico 1.16 in 97.2 seconds.