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

generates a code of length 83 over Z5[X]/(X^2) who´s minimum homogenous weight is 320.

Homogenous weight enumerator: w(x)=1x^0+92x^320+440x^325+1092x^330+1348x^335+72x^340+24x^345+16x^350+8x^355+8x^360+8x^365+4x^370+4x^375+4x^385+4x^400

The gray image is a linear code over GF(5) with n=415, k=5 and d=320.
This code was found by Heurico 1.16 in 0.139 seconds.