The generator matrix

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

generates a code of length 88 over Z5[X]/(X^2) who´s minimum homogenous weight is 351.

Homogenous weight enumerator: w(x)=1x^0+160x^351+400x^352+40x^356+16x^365+8x^370

The gray image is a linear code over GF(5) with n=440, k=4 and d=351.
This code was found by Heurico 1.16 in 0.101 seconds.