The generator matrix

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

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+262x^56+96x^58+96x^60+54x^64+3x^80

The gray image is a code over GF(2) with n=232, k=9 and d=112.
This code was found by Heurico 1.16 in 0.191 seconds.