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

generates a code of length 76 over Z5[X]/(X^2) who´s minimum homogenous weight is 270.

Homogenous weight enumerator: w(x)=1x^0+236x^270+680x^275+996x^280+20x^284+1344x^285+400x^289+1204x^290+3200x^294+1296x^295+12800x^299+1492x^300+25600x^304+1676x^305+20480x^309+1548x^310+1512x^315+1216x^320+964x^325+696x^330+388x^335+224x^340+112x^345+28x^350+12x^355

The gray image is a linear code over GF(5) with n=380, k=7 and d=270.
This code was found by Heurico 1.16 in 31.6 seconds.