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

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+1008x^300+1700x^301+920x^302+160x^303+540x^304+2852x^305+4700x^306+2080x^307+420x^308+940x^309+4288x^310+7380x^311+2580x^312+640x^313+1120x^314+4916x^315+7760x^316+2580x^317+560x^318+1100x^319+4700x^320+6840x^321+2180x^322+480x^323+980x^324+3544x^325+4820x^326+1660x^327+240x^328+320x^329+1448x^330+1800x^331+500x^332+324x^335+16x^340+12x^345+4x^350+12x^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 18.4 seconds.