The generator matrix

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

generates a code of length 79 over Z5[X]/(X^2) who´s minimum homogenous weight is 300.

Homogenous weight enumerator: w(x)=1x^0+1056x^300+1180x^301+1200x^302+300x^303+340x^304+3776x^305+4300x^306+2400x^307+380x^308+340x^309+5900x^310+5120x^311+2960x^312+640x^313+580x^314+6484x^315+6240x^316+3060x^317+340x^318+620x^319+6540x^320+5560x^321+2960x^322+440x^323+460x^324+4644x^325+3600x^326+1860x^327+340x^328+160x^329+2016x^330+1500x^331+560x^332+60x^333+160x^335+16x^340+20x^345+4x^350+8x^355

The gray image is a linear code over GF(5) with n=395, k=7 and d=300.
This code was found by Heurico 1.16 in 22.8 seconds.