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

generates a code of length 79 over Z5[X]/(X^2) who´s minimum homogenous weight is 280.

Homogenous weight enumerator: w(x)=1x^0+132x^280+536x^285+876x^290+1168x^295+1380x^300+2932x^305+11120x^310+27036x^315+27136x^320+1460x^325+1356x^330+1064x^335+840x^340+556x^345+280x^350+160x^355+80x^360+8x^365+4x^375

The gray image is a linear code over GF(5) with n=395, k=7 and d=280.
This code was found by Heurico 1.16 in 32.9 seconds.