The generator matrix

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

generates a code of length 83 over Z5[X]/(X^2) who´s minimum homogenous weight is 327.

Homogenous weight enumerator: w(x)=1x^0+220x^327+48x^330+160x^332+60x^335+20x^337+8x^340+100x^342+4x^345+4x^365

The gray image is a linear code over GF(5) with n=415, k=4 and d=327.
This code was found by Heurico 1.16 in 0.0975 seconds.