The generator matrix

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

generates a code of length 88 over Z5[X]/(X^2) who´s minimum homogenous weight is 335.

Homogenous weight enumerator: w(x)=1x^0+952x^335+680x^336+980x^337+240x^338+560x^339+3916x^340+2220x^341+2660x^342+980x^343+1020x^344+5692x^345+3320x^346+3520x^347+1200x^348+720x^349+6772x^350+4040x^351+3360x^352+840x^353+1120x^354+6664x^355+3140x^356+3380x^357+880x^358+920x^359+5280x^360+2460x^361+2420x^362+580x^363+460x^364+3048x^365+1320x^366+1160x^367+280x^368+200x^369+756x^370+320x^371+20x^372+20x^375+4x^380+8x^390+4x^395+4x^400+4x^405

The gray image is a linear code over GF(5) with n=440, k=7 and d=335.
This code was found by Heurico 1.16 in 14.7 seconds.