The generator matrix

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

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+144x^350+100x^352+176x^355+800x^357+132x^360+1600x^362+52x^365+40x^370+40x^375+8x^380+8x^385+8x^390+4x^395+4x^400+4x^410+4x^440

The gray image is a linear code over GF(5) with n=450, k=5 and d=350.
This code was found by Heurico 1.16 in 0.173 seconds.