The generator matrix

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

generates a code of length 80 over Z5[X]/(X^2) who´s minimum homogenous weight is 315.

Homogenous weight enumerator: w(x)=1x^0+220x^315+1320x^316+248x^320+740x^321+104x^325+120x^326+260x^331+40x^335+60x^336+12x^345

The gray image is a linear code over GF(5) with n=400, k=5 and d=315.
This code was found by Heurico 1.16 in 30.8 seconds.