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

generates a code of length 89 over Z5[X]/(X^2) who´s minimum homogenous weight is 330.

Homogenous weight enumerator: w(x)=1x^0+68x^330+292x^335+436x^340+100x^341+456x^345+600x^346+332x^350+2600x^351+360x^355+5100x^356+236x^360+4100x^361+212x^365+144x^370+164x^375+116x^380+108x^385+44x^390+56x^395+28x^400+36x^405+24x^410+8x^415+4x^420

The gray image is a linear code over GF(5) with n=445, k=6 and d=330.
This code was found by Heurico 1.16 in 1.64 seconds.