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

generates a code of length 89 over Z5[X]/(X^2) who´s minimum homogenous weight is 345.

Homogenous weight enumerator: w(x)=1x^0+92x^345+220x^350+116x^355+2500x^356+48x^360+48x^365+56x^370+12x^375+16x^380+4x^385+4x^390+4x^400+4x^445

The gray image is a linear code over GF(5) with n=445, k=5 and d=345.
This code was found by Heurico 1.16 in 0.167 seconds.