The generator matrix

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

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+812x^345+1040x^346+360x^347+580x^348+1768x^350+1740x^351+380x^352+520x^353+1220x^355+1180x^356+300x^357+460x^358+956x^360+900x^361+200x^362+160x^363+588x^365+620x^366+180x^367+120x^368+576x^370+400x^371+80x^372+160x^373+200x^375+120x^376+4x^390

The gray image is a linear code over GF(5) with n=445, k=6 and d=345.
This code was found by Heurico 1.16 in 0.615 seconds.