The generator matrix

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

generates a code of length 76 over Z5[X]/(X^2) who´s minimum homogenous weight is 290.

Homogenous weight enumerator: w(x)=1x^0+192x^290+320x^291+860x^294+1160x^295+1120x^296+880x^299+1336x^300+1060x^301+1200x^304+956x^305+900x^306+1520x^309+1196x^310+1040x^311+540x^314+568x^315+460x^316+156x^320+100x^321+16x^325+20x^330+4x^335+4x^345+12x^350+4x^355

The gray image is a linear code over GF(5) with n=380, k=6 and d=290.
This code was found by Heurico 1.16 in 0.6 seconds.