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  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  X  1  1  X  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  0  0  X  X 4X 2X 3X 4X 3X 3X 3X 2X 2X  0  0 2X 2X 3X 3X 2X 2X 2X  0  0 2X 3X 4X 3X  0 3X 2X 3X 4X 4X 2X  X 4X  0 4X 4X 4X  0 4X 2X  0 3X 2X 3X  X  0 3X 2X  0  X 3X 2X 4X  X  X  0  X 4X  0 4X 3X  0 2X  X  X  0
 0  0  X  0  0  X  X 3X 4X 3X  0  X 2X 2X 4X  0 4X  X  X  0  X 3X  X 3X 4X  0 2X 2X 2X  X 4X 4X  X 3X 3X 4X 2X 4X  X  0  X  0  0  0  X  0 2X  0 2X 2X 2X 3X 2X  X  0 2X 4X  X  X 3X 4X 3X  X 4X 2X 4X 2X  X 3X  X 2X 2X 2X 3X  0
 0  0  0  X  0 3X 2X 3X  X  X 4X  X  0  X 2X  X  X 2X 3X 2X  X  0  X 4X 3X 2X 4X 2X 3X 2X 2X 4X  0 3X 2X  0 2X 3X  X  X  0 4X 4X  0 3X 4X  X  X  X  X 2X 4X 4X  X  X 3X 2X 2X 3X  X 4X 2X 4X  0 4X 3X 2X 2X 2X 3X 4X  0  0 3X  0
 0  0  0  0  X 3X  X 4X 3X  X 3X 4X 2X  0  0  X  0 3X 2X  X  X 4X  X 2X  0 4X  0 4X  X 4X  X 2X 4X 2X 3X 2X 4X 3X 3X 4X 4X 4X 4X  X  X  0 4X  X  0 3X 2X 3X 4X 2X 2X 2X 3X 2X  0 3X  0 4X  0  0  0 2X 2X  0 3X 2X 2X  0  0 2X  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+76x^275+324x^280+468x^285+100x^288+392x^290+1200x^293+340x^295+4800x^298+316x^300+6400x^303+264x^305+284x^310+180x^315+92x^320+104x^325+132x^330+64x^335+48x^340+28x^345+8x^350+4x^360

The gray image is a linear code over GF(5) with n=375, k=6 and d=275.
This code was found by Heurico 1.16 in 1.28 seconds.