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

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+1000x^331+900x^332+740x^333+580x^334+596x^335+4020x^336+2000x^337+1820x^338+1060x^339+956x^340+5760x^341+3520x^342+2360x^343+1880x^344+1260x^345+7800x^346+3460x^347+2700x^348+1300x^349+1072x^350+6600x^351+3440x^352+2480x^353+1320x^354+1012x^355+6000x^356+2620x^357+1520x^358+1160x^359+584x^360+3080x^361+1200x^362+820x^363+200x^364+76x^365+740x^366+360x^367+60x^368+20x^370+28x^375+8x^380+8x^390+4x^400

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 19.3 seconds.