The generator matrix

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

generates a code of length 92 over Z5[X]/(X^2) who´s minimum homogenous weight is 345.

Homogenous weight enumerator: w(x)=1x^0+572x^345+640x^346+1000x^347+660x^348+2500x^349+5080x^350+3440x^351+3680x^352+2960x^353+6500x^354+9432x^355+7240x^356+6880x^357+5080x^358+10300x^359+16244x^360+12000x^361+11240x^362+7420x^363+13860x^364+22932x^365+16400x^366+13360x^367+8920x^368+17180x^369+27292x^370+18260x^371+14960x^372+8600x^373+16080x^374+22996x^375+14400x^376+11280x^377+6340x^378+9480x^379+12928x^380+6240x^381+4380x^382+2260x^383+3480x^384+2804x^385+1320x^386+720x^387+260x^388+620x^389+296x^390+60x^391+24x^395+16x^400+8x^405

The gray image is a linear code over GF(5) with n=460, k=8 and d=345.
This code was found by Heurico 1.16 in 344 seconds.