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

generates a code of length 80 over Z5[X]/(X^2) who´s minimum homogenous weight is 285.

Homogenous weight enumerator: w(x)=1x^0+180x^285+684x^290+976x^295+1108x^300+300x^301+1212x^305+1200x^306+1528x^310+4200x^311+1504x^315+14700x^316+1444x^320+26700x^321+1528x^325+15400x^326+1368x^330+1284x^335+1048x^340+756x^345+468x^350+320x^355+148x^360+64x^365+4x^370

The gray image is a linear code over GF(5) with n=400, k=7 and d=285.
This code was found by Heurico 1.16 in 33.6 seconds.