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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  0  2  2  0  2  2  2  0  2  0  2  2  2  0  2  0  2  2  0  2  2  0  2  0  2  0  2  0  2  2  0  2  0  2  2
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  0  2  2  0  2  2  0  0  2  2  2  0  2  0  2  2  2  2  0  2  2  0  2  0  2  2  0  2  2  2  0  2  2  2  2  0
 0  0  0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  0  2  2  2  2  0  2  2  0  2  2  0  2  0  2  0  0  2  2  2  2  2  0  0  0  0  2  0  0  2  2  2  0  0  2  2  2  2  0
 0  0  0  0  2  0  0  0  2  2  2  2  2  0  2  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  0  2  2  0  2  2  0  0  0  2  2  2  2  0  2  2  0  2  2  2  2  2  2  2  0  2
 0  0  0  0  0  2  0  2  2  2  0  0  0  0  2  2  2  0  0  0  0  0  0  0  2  2  2  0  0  2  2  0  2  2  2  0  2  0  2  0  0  2  2  2  2  2  2  0  0  0  2  2  2  0  2  2
 0  0  0  0  0  0  2  2  0  2  2  0  2  2  2  0  0  0  0  0  0  2  2  2  2  2  0  2  0  0  2  0  0  0  2  2  0  2  0  2  0  0  0  2  2  2  2  0  0  2  2  0  2  2  0  0

generates a code of length 56 over Z4 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+36x^52+182x^56+36x^60+1x^112

The gray image is a code over GF(2) with n=112, k=8 and d=52.
This code was found by Heurico 1.16 in 0.0563 seconds.