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

generates a code of length 92 over Z5[X]/(X^2) who´s minimum homogenous weight is 351.

Homogenous weight enumerator: w(x)=1x^0+1020x^351+1280x^352+1100x^353+108x^355+3860x^356+3520x^357+2000x^358+120x^360+5680x^361+6100x^362+3220x^363+120x^365+6600x^366+6240x^367+3160x^368+136x^370+5980x^371+5900x^372+2040x^373+36x^375+5440x^376+4380x^377+2220x^378+20x^380+3080x^381+2000x^382+1000x^383+16x^385+840x^386+580x^387+260x^388+28x^390+8x^395+16x^400+12x^410+4x^420

The gray image is a linear code over GF(5) with n=460, k=7 and d=351.
This code was found by Heurico 1.16 in 58 seconds.