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 2X  1  1 2X  1  1  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 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  X  1  2  3 3X 4X+2  1 4X+4  0 X+2 X+1 X+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  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 4X+2 4X+4 3X+4  4  1 4X+1 3X+2 2X 4X+4 X+3 X+1 4X+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+1100x^341+500x^342+260x^343+1160x^344+52x^345+1900x^346+880x^347+280x^348+1120x^349+1760x^351+560x^352+140x^353+720x^354+28x^355+980x^356+460x^357+140x^358+400x^359+8x^360+860x^361+380x^362+80x^363+360x^364+24x^365+700x^366+220x^367+100x^368+240x^369+8x^370+200x^371+4x^380

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 38 seconds.