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

generates a code of length 81 over Z5[X]/(X^2) who´s minimum homogenous weight is 315.

Homogenous weight enumerator: w(x)=1x^0+232x^315+100x^316+112x^320+800x^321+108x^325+1600x^326+68x^330+36x^335+20x^340+12x^345+12x^350+8x^355+4x^365+8x^370+4x^395

The gray image is a linear code over GF(5) with n=405, k=5 and d=315.
This code was found by Heurico 1.16 in 61.1 seconds.