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

generates a code of length 86 over Z5[X]/(X^2) who´s minimum homogenous weight is 327.

Homogenous weight enumerator: w(x)=1x^0+700x^327+1040x^328+500x^329+804x^330+460x^331+3560x^332+3100x^333+1520x^334+1840x^335+940x^336+4540x^337+4420x^338+1980x^339+2204x^340+960x^341+5860x^342+5440x^343+2120x^344+1952x^345+1040x^346+5220x^347+5300x^348+1980x^349+1972x^350+1020x^351+3980x^352+3920x^353+1240x^354+1432x^355+540x^356+2980x^357+1520x^358+580x^359+384x^360+40x^361+660x^362+260x^363+80x^364+8x^370+12x^375+8x^380+4x^395+4x^400

The gray image is a linear code over GF(5) with n=430, k=7 and d=327.
This code was found by Heurico 1.16 in 14.3 seconds.