The generator matrix

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

generates a code of length 89 over Z5[X]/(X^2) who´s minimum homogenous weight is 344.

Homogenous weight enumerator: w(x)=1x^0+1320x^344+500x^345+2840x^349+804x^350+2740x^354+548x^355+2260x^359+508x^360+1980x^364+524x^365+1180x^369+156x^370+180x^374+32x^375+20x^380+4x^385+8x^390+16x^395+4x^405

The gray image is a linear code over GF(5) with n=445, k=6 and d=344.
This code was found by Heurico 1.16 in 33.2 seconds.