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

generates a code of length 90 over Z5[X]/(X^2) who´s minimum homogenous weight is 338.

Homogenous weight enumerator: w(x)=1x^0+360x^338+1460x^339+2080x^340+1880x^341+1960x^342+2700x^343+5660x^344+7312x^345+4660x^346+4160x^347+5960x^348+11540x^349+12168x^350+8540x^351+7300x^352+9560x^353+15740x^354+17288x^355+12380x^356+10400x^357+13580x^358+20880x^359+22360x^360+13560x^361+12380x^362+15340x^363+21920x^364+23788x^365+13360x^366+9740x^367+11720x^368+16920x^369+14508x^370+7560x^371+5160x^372+4880x^373+7140x^374+5432x^375+2760x^376+1340x^377+900x^378+1240x^379+636x^380+300x^381+60x^382+24x^385+16x^390+4x^395+8x^400

The gray image is a linear code over GF(5) with n=450, k=8 and d=338.
This code was found by Heurico 1.16 in 407 seconds.