The generator matrix

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

generates a code of length 90 over Z5[X]/(X^2) who´s minimum homogenous weight is 344.

Homogenous weight enumerator: w(x)=1x^0+2720x^344+976x^345+8540x^349+2272x^350+11280x^354+3260x^355+12520x^359+3000x^360+12480x^364+2828x^365+9420x^369+2084x^370+4460x^374+1084x^375+1080x^379+88x^380+12x^385+4x^390+12x^395+4x^405

The gray image is a linear code over GF(5) with n=450, k=7 and d=344.
This code was found by Heurico 1.16 in 270 seconds.