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

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+400x^291+320x^292+580x^293+1240x^294+524x^295+3100x^296+2040x^297+2300x^298+2140x^299+1004x^300+4840x^301+2680x^302+3240x^303+3300x^304+1352x^305+5720x^306+3320x^307+3060x^308+3100x^309+1108x^310+6340x^311+3360x^312+2780x^313+2700x^314+912x^315+4660x^316+2480x^317+2320x^318+1960x^319+516x^320+2180x^321+800x^322+720x^323+560x^324+140x^325+260x^326+16x^330+20x^335+16x^340+8x^345+8x^350

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 13.2 seconds.