The generator matrix

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

generates a code of length 87 over Z5[X]/(X^2) who´s minimum homogenous weight is 331.

Homogenous weight enumerator: w(x)=1x^0+880x^331+820x^332+1100x^333+420x^334+756x^335+3300x^336+2300x^337+2500x^338+700x^339+1420x^340+5440x^341+3140x^342+3400x^343+1120x^344+1808x^345+5960x^346+3780x^347+3680x^348+980x^349+1568x^350+6180x^351+3220x^352+3240x^353+940x^354+1748x^355+4820x^356+2540x^357+2400x^358+680x^359+652x^360+2820x^361+1400x^362+1060x^363+160x^364+100x^365+600x^366+300x^367+120x^368+20x^370+24x^375+20x^380+8x^390

The gray image is a linear code over GF(5) with n=435, k=7 and d=331.
This code was found by Heurico 1.16 in 25.1 seconds.