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

generates a code of length 86 over Z5[X]/(X^2) who´s minimum homogenous weight is 310.

Homogenous weight enumerator: w(x)=1x^0+400x^310+692x^315+1028x^320+1368x^325+2352x^330+6608x^335+16396x^340+26244x^345+17756x^350+1356x^355+1204x^360+884x^365+788x^370+516x^375+332x^380+128x^385+48x^390+20x^395+4x^400

The gray image is a linear code over GF(5) with n=430, k=7 and d=310.
This code was found by Heurico 1.16 in 38 seconds.