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

generates a code of length 85 over Z5[X]/(X^2) who´s minimum homogenous weight is 305.

Homogenous weight enumerator: w(x)=1x^0+272x^305+668x^310+1008x^315+40x^318+1208x^320+680x^323+1192x^325+2800x^328+1356x^330+9200x^333+1412x^335+18200x^338+1476x^340+21160x^343+1520x^345+10420x^348+1384x^350+1264x^355+1040x^360+712x^365+520x^370+288x^375+168x^380+100x^385+24x^390+12x^395

The gray image is a linear code over GF(5) with n=425, k=7 and d=305.
This code was found by Heurico 1.16 in 35 seconds.