The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X  0  X  0  X  0  X  X  X  X  X  X  X  2  X  2  X  2  X  0  X  0  2  X
 0  X  0 X+2  0 X+2  0  X  0 X+2  0  X  0 X+2  0  X  2 X+2  2  X  2 X+2  2  X  2 X+2  2  X  2 X+2  2  X X+2  X X+2  X X+2  X X+2  X  0  0  2  2  0  2  X  X  X  X  0  0 X+2  X X+2  2  X  0
 0  0  2  0  0  0  2  0  0  2  0  2  2  2  2  2  2  0  2  0  2  0  2  0  0  2  0  2  0  2  0  2  0  0  0  0  2  2  2  2  0  2  2  0  2  2  2  2  2  2  2  2  2  2  2  2  2  2
 0  0  0  2  0  0  0  2  2  2  2  2  2  0  2  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  2  2  2  2  0  0  2  2  2  2  0  0  0  0  2  2  2  2  2  2  0  2  0  2
 0  0  0  0  2  2  2  2  2  0  0  2  0  2  2  0  0  0  2  2  2  2  0  0  0  2  2  0  2  0  0  2  0  2  2  0  0  2  2  0  2  0  0  2  2  2  2  0  0  2  2  2  2  0  0  2  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+148x^56+80x^60+23x^64+4x^72

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 0.112 seconds.