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

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+84x^340+196x^345+500x^348+92x^350+2000x^353+104x^355+76x^360+12x^365+12x^370+20x^375+4x^380+8x^385+12x^390+4x^435

The gray image is a linear code over GF(5) with n=440, k=5 and d=340.
This code was found by Heurico 1.16 in 0.162 seconds.