The generator matrix

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

generates a code of length 75 over Z5[X]/(X^2) who´s minimum homogenous weight is 275.

Homogenous weight enumerator: w(x)=1x^0+92x^275+20x^278+616x^280+160x^281+240x^283+2420x^285+1320x^286+1280x^288+4224x^290+2740x^291+1780x^293+6772x^295+5140x^296+2680x^298+10520x^300+7540x^301+3460x^303+9428x^305+5980x^306+2440x^308+4960x^310+2120x^311+600x^313+1048x^315+188x^320+168x^325+52x^330+60x^335+48x^340+20x^345+4x^350+4x^355

The gray image is a linear code over GF(5) with n=375, k=7 and d=275.
This code was found by Heurico 1.16 in 13.6 seconds.