The generator matrix

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

generates a code of length 90 over Z5[X]/(X^2) who´s minimum homogenous weight is 350.

Homogenous weight enumerator: w(x)=1x^0+2800x^350+4520x^355+3020x^360+2180x^365+1540x^370+1324x^375+240x^380

The gray image is a linear code over GF(5) with n=450, k=6 and d=350.
This code was found by Heurico 1.16 in 1.06 seconds.