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  1 4X  1  1  1  1  1  0 3X 3X  1  X  1  0  1  1  1  1  1  X
 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  0 4X 2X+3  4 3X+3 X+4  1 3X+2 4X+2 X+3 2X+4  4  1  1  1 X+4  1 3X+3  1 3X+3 2X+4 X+2  1 2X+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 2X+1 X+1 X+4 3X+3  2 4X+2  0 2X+2 2X+1 2X 3X 4X+4 4X 2X+2  1 3X+3 2X+4 3X+4 4X+2 2X+1 X+3 X+4 4X+2 4X+1 X+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  0  X 4X 2X 2X 3X 3X 2X 3X 3X 4X 4X 4X  0  0  X 3X 3X  X  X 2X  0 4X 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+2500x^344+1088x^345+8540x^349+2068x^350+11640x^354+3116x^355+13080x^359+3288x^360+11740x^364+3016x^365+9300x^369+1876x^370+4420x^374+968x^375+1280x^379+164x^380+16x^385+8x^390+12x^400+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 96.9 seconds.