The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1 X+2  1  1  1  1  2  X  1  1  1  1  1  1  1  1  1  1  1  1  2  X  2  X  2  X  1  1  1  1  1  1  1  1  2  1
 0  1 X+1 X+2  3  1  0 X+1  1 X+2  3  1  0 X+1  1 X+2  3  1  0 X+1  1 X+2  3  1  2  X X+3  1  1  1  2  X X+3  1  2  X  2  X X+3  1 X+3  1  1  1  1  1  1  1  0 X+2  0 X+2  0  2 X+2  X  2  0
 0  0  2  0  2  0  2  0  2  2  0  2  0  0  0  2  0  0  2  2  2  0  2  2  2  2  2  2  2  2  0  0  0  0  2  2  0  0  2  2  0  0  0  0  2  2  0  0  0  0  2  2  0  2  0  2  0  0
 0  0  0  2  2  2  2  0  0  0  2  2  2  2  2  2  0  0  0  2  2  0  0  0  0  2  0  2  0  2  2  0  2  0  2  0  0  2  2  0  0  2  2  0  2  0  0  2  0  2  2  0  2  0  0  2  0  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+26x^56+112x^57+18x^58+64x^59+4x^60+16x^61+12x^62+1x^64+2x^82

The gray image is a code over GF(2) with n=232, k=8 and d=112.
This code was found by Heurico 1.16 in 0.0766 seconds.