The generator matrix

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

generates a code of length 58 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+715x^52+1212x^54+1663x^56+1428x^58+1334x^60+964x^62+605x^64+172x^66+95x^68+3x^72

The gray image is a code over GF(2) with n=232, k=13 and d=104.
This code was found by Heurico 1.16 in 50.4 seconds.