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

generates a code of length 94 over Z5[X]/(X^2) who´s minimum homogenous weight is 350.

Homogenous weight enumerator: w(x)=1x^0+104x^350+140x^354+556x^355+540x^356+900x^359+1740x^360+1320x^361+2120x^364+2928x^365+2980x^366+3740x^369+4280x^370+4700x^371+5480x^374+5704x^375+5180x^376+6240x^379+6240x^380+5240x^381+4380x^384+4224x^385+3660x^386+1760x^389+1560x^390+1300x^391+240x^394+352x^395+80x^396+132x^400+84x^405+72x^410+68x^415+28x^420+24x^425+20x^430+4x^435+4x^440

The gray image is a linear code over GF(5) with n=470, k=7 and d=350.
This code was found by Heurico 1.16 in 17.7 seconds.