The generator matrix

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

generates a code of length 36 over Z5[X]/(X^2) who´s minimum homogenous weight is 127.

Homogenous weight enumerator: w(x)=1x^0+740x^127+1580x^128+1140x^129+468x^130+2500x^131+4780x^132+8620x^133+4760x^134+2712x^135+8580x^136+13060x^137+20480x^138+11680x^139+6432x^140+19260x^141+29740x^142+39040x^143+23500x^144+11148x^145+30740x^146+38520x^147+43100x^148+18220x^149+7224x^150+13920x^151+13160x^152+12180x^153+3200x^154+48x^155+48x^160+28x^165+12x^170+4x^180

The gray image is a linear code over GF(5) with n=180, k=8 and d=127.
This code was found by Heurico 1.16 in 112 seconds.