The generator matrix

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

generates a code of length 75 over Z5[X]/(X^2) who´s minimum homogenous weight is 265.

Homogenous weight enumerator: w(x)=1x^0+140x^265+580x^270+940x^275+1208x^280+1696x^285+4616x^290+14344x^295+27088x^300+22064x^305+1524x^310+1232x^315+1024x^320+808x^325+448x^330+260x^335+112x^340+32x^345+8x^350

The gray image is a linear code over GF(5) with n=375, k=7 and d=265.
This code was found by Heurico 1.16 in 30.9 seconds.