The generator matrix

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

generates a code of length 85 over Z5[X]/(X^2) who´s minimum homogenous weight is 315.

Homogenous weight enumerator: w(x)=1x^0+96x^315+20x^318+636x^320+240x^321+280x^322+820x^323+1312x^325+1780x^326+620x^327+1980x^328+1988x^330+3020x^331+1840x^332+3360x^333+2436x^335+4480x^336+2740x^337+6060x^338+2736x^340+6780x^341+3340x^342+7140x^343+2752x^345+5840x^346+2960x^347+4140x^348+2040x^350+2600x^351+720x^352+1480x^353+1036x^355+260x^356+200x^360+100x^365+92x^370+68x^375+56x^380+44x^385+28x^390+4x^400

The gray image is a linear code over GF(5) with n=425, k=7 and d=315.
This code was found by Heurico 1.16 in 15.7 seconds.