The generator matrix

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

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+20x^56+68x^57+88x^58+56x^59+10x^60+4x^61+6x^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 0.0761 seconds.