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

generates a code of length 88 over Z5[X]/(X^2) who´s minimum homogenous weight is 341.

Homogenous weight enumerator: w(x)=1x^0+840x^341+600x^342+580x^343+520x^344+328x^345+2160x^346+940x^347+820x^348+360x^349+368x^350+1360x^351+780x^352+340x^353+200x^354+152x^355+1160x^356+520x^357+280x^358+160x^359+160x^360+640x^361+360x^362+240x^363+140x^364+88x^365+560x^366+300x^367+240x^368+120x^369+28x^370+280x^371

The gray image is a linear code over GF(5) with n=440, k=6 and d=341.
This code was found by Heurico 1.16 in 2.22 seconds.