The generator matrix

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

generates a code of length 83 over Z5[X]/(X^2) who´s minimum homogenous weight is 315.

Homogenous weight enumerator: w(x)=1x^0+520x^315+1280x^316+300x^317+320x^318+1500x^319+2436x^320+4120x^321+600x^322+880x^323+3080x^324+3460x^325+5180x^326+900x^327+1080x^328+3680x^329+4472x^330+6180x^331+1300x^332+920x^333+4060x^334+4208x^335+6520x^336+1000x^337+1060x^338+3240x^339+3244x^340+3880x^341+700x^342+480x^343+1720x^344+1740x^345+2380x^346+200x^347+260x^348+220x^349+484x^350+460x^351+28x^355+12x^360+16x^365+4x^370

The gray image is a linear code over GF(5) with n=415, k=7 and d=315.
This code was found by Heurico 1.16 in 12.9 seconds.