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

generates a code of length 88 over Z5[X]/(X^2) who´s minimum homogenous weight is 340.

Homogenous weight enumerator: w(x)=1x^0+1644x^340+3580x^345+3220x^350+3112x^355+2648x^360+1108x^365+264x^370+8x^375+4x^380+4x^385+4x^390+12x^395+12x^400+4x^410

The gray image is a linear code over GF(5) with n=440, k=6 and d=340.
This code was found by Heurico 1.16 in 20.7 seconds.