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

generates a code of length 77 over Z5[X]/(X^2) who´s minimum homogenous weight is 275.

Homogenous weight enumerator: w(x)=1x^0+384x^275+700x^280+20x^284+1064x^285+1332x^290+1200x^294+1340x^295+4800x^299+1412x^300+15600x^304+1520x^305+24480x^309+1360x^310+16400x^314+1568x^315+1368x^320+1264x^325+1012x^330+632x^335+400x^340+172x^345+64x^350+28x^355+4x^360

The gray image is a linear code over GF(5) with n=385, k=7 and d=275.
This code was found by Heurico 1.16 in 32.4 seconds.