The generator matrix

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

generates a code of length 89 over Z5[X]/(X^2) who´s minimum homogenous weight is 340.

Homogenous weight enumerator: w(x)=1x^0+3324x^340+10188x^345+14816x^350+16088x^355+14940x^360+11756x^365+5728x^370+1252x^375+12x^380+4x^385+4x^390+8x^395+4x^405

The gray image is a linear code over GF(5) with n=445, k=7 and d=340.
This code was found by Heurico 1.16 in 68.8 seconds.