The generator matrix

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

generates a code of length 91 over Z5[X]/(X^2) who´s minimum homogenous weight is 347.

Homogenous weight enumerator: w(x)=1x^0+1000x^347+1340x^348+560x^349+116x^350+4860x^352+3900x^353+1020x^354+80x^355+7280x^357+5500x^358+1440x^359+116x^360+7740x^362+6300x^363+1580x^364+120x^365+8060x^367+5820x^368+1320x^369+76x^370+6280x^372+4400x^373+1000x^374+20x^375+3740x^377+2260x^378+480x^379+28x^380+1040x^382+480x^383+100x^384+36x^385+12x^390+4x^400+8x^405+4x^410+4x^415

The gray image is a linear code over GF(5) with n=455, k=7 and d=347.
This code was found by Heurico 1.16 in 15 seconds.