The generator matrix

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

generates a code of length 78 over Z5[X]/(X^2) who´s minimum homogenous weight is 295.

Homogenous weight enumerator: w(x)=1x^0+536x^295+560x^296+700x^297+140x^298+1420x^299+3588x^300+1800x^301+2160x^302+560x^303+2500x^304+5472x^305+2780x^306+2760x^307+400x^308+3040x^309+6344x^310+3320x^311+3640x^312+440x^313+3320x^314+6576x^315+3160x^316+3120x^317+580x^318+3200x^319+4948x^320+2340x^321+1800x^322+280x^323+1460x^324+2652x^325+940x^326+820x^327+100x^328+60x^329+464x^330+100x^331+20x^335+8x^340+8x^350+8x^355

The gray image is a linear code over GF(5) with n=390, k=7 and d=295.
This code was found by Heurico 1.16 in 12.7 seconds.