The generator matrix

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

generates a code of length 79 over Z5[X]/(X^2) who´s minimum homogenous weight is 290.

Homogenous weight enumerator: w(x)=1x^0+68x^290+60x^292+20x^294+348x^295+340x^297+160x^298+680x^299+844x^300+1260x^302+980x^303+2200x^304+1880x^305+3220x^307+1560x^308+3780x^309+2236x^310+4740x^312+2560x^313+5180x^314+3248x^315+6780x^317+3760x^318+7160x^319+3396x^320+5800x^322+2700x^323+4800x^324+2392x^325+2580x^327+780x^328+1180x^329+672x^330+220x^332+148x^335+104x^340+100x^345+88x^350+28x^355+36x^360+20x^365+16x^370

The gray image is a linear code over GF(5) with n=395, k=7 and d=290.
This code was found by Heurico 1.16 in 14.5 seconds.