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

generates a code of length 76 over Z5[X]/(X^2) who´s minimum homogenous weight is 287.

Homogenous weight enumerator: w(x)=1x^0+400x^287+860x^288+220x^289+420x^290+1200x^291+2440x^292+3980x^293+760x^294+1032x^295+2160x^296+4180x^297+6140x^298+1040x^299+1220x^300+2740x^301+4600x^302+6960x^303+940x^304+848x^305+2600x^306+4900x^307+7580x^308+1040x^309+1216x^310+2160x^311+3800x^312+5340x^313+820x^314+536x^315+1420x^316+1960x^317+1640x^318+180x^319+304x^320+220x^321+220x^322+24x^325+4x^330+4x^335+4x^340+4x^345+8x^355

The gray image is a linear code over GF(5) with n=380, k=7 and d=287.
This code was found by Heurico 1.16 in 11.7 seconds.