The generator matrix

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

generates a code of length 77 over Z5[X]/(X^2) who´s minimum homogenous weight is 291.

Homogenous weight enumerator: w(x)=1x^0+320x^291+500x^292+1120x^293+1020x^294+496x^295+2020x^296+2420x^297+3000x^298+1880x^299+1156x^300+2980x^301+3800x^302+5060x^303+2540x^304+1128x^305+3460x^306+4620x^307+4480x^308+2700x^309+1164x^310+4040x^311+4340x^312+4300x^313+2360x^314+1008x^315+3200x^316+3160x^317+3500x^318+1500x^319+452x^320+1380x^321+1160x^322+1040x^323+500x^324+156x^325+100x^326+20x^330+4x^335+20x^340+20x^345

The gray image is a linear code over GF(5) with n=385, k=7 and d=291.
This code was found by Heurico 1.16 in 11.9 seconds.