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

generates a code of length 88 over Z5[X]/(X^2) who´s minimum homogenous weight is 330.

Homogenous weight enumerator: w(x)=1x^0+296x^330+436x^335+548x^340+1532x^345+5152x^350+6620x^355+260x^360+144x^365+180x^370+144x^375+76x^380+84x^385+64x^390+48x^395+24x^400+8x^405+4x^415+4x^425

The gray image is a linear code over GF(5) with n=440, k=6 and d=330.
This code was found by Heurico 1.16 in 20.7 seconds.