The generator matrix

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

generates a code of length 81 over Z5[X]/(X^2) who´s minimum homogenous weight is 308.

Homogenous weight enumerator: w(x)=1x^0+2000x^308+1240x^309+284x^310+6280x^313+3440x^314+608x^315+8980x^318+4800x^319+552x^320+10820x^323+5900x^324+508x^325+10560x^328+5100x^329+632x^330+7600x^333+3260x^334+348x^335+3260x^338+1260x^339+136x^340+500x^343+20x^345+8x^350+20x^360+8x^365

The gray image is a linear code over GF(5) with n=405, k=7 and d=308.
This code was found by Heurico 1.16 in 82.2 seconds.