The generator matrix

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

generates a code of length 58 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+732x^56+64x^60+223x^64+4x^72

The gray image is a code over GF(2) with n=232, k=10 and d=112.
This code was found by Heurico 1.16 in 12.4 seconds.