The generator matrix

 1  0  0  0  1  1  1  2  1  1  2  1  2  0  1  1  0  0  0  1  1  1  1  1  1  1  1  0  2  0  2  1  2  1  2  1  1  2  0  2  0  1  0  2  0  2  1  2  0  2  1  2  1  1  2  0
 0  1  0  0  0  0  0  0  1  3  1  3  1  1  1  2  1  1  2  2  1  1  2  3  0  3  2  1  2  1  2  2  2  0  0  3  1  1  1  0  0  3  0  0  1  1  2  2  2  2  2  2  1  0  1  1
 0  0  1  0  0  1  3  1  1  1  2  0  3  3  0  0  2  1  1  3  3  0  2  2  1  3  3  2  2  1  1  0  1  0  1  0  0  2  2  1  1  0  1  1  0  2  1  2  2  0  1  0  2  1  1  3
 0  0  0  1  1  3  0  1  0  1  1  0  0  3  3  2  1  2  3  3  2  3  3  2  3  3  0  2  1  1  0  2  3  2  3  3  1  3  3  1  3  0  2  2  3  1  3  1  1  1  2  1  2  0  3  3
 0  0  0  0  2  2  2  0  2  2  0  2  0  0  2  2  0  0  0  2  2  0  0  0  0  0  0  2  2  2  2  0  0  0  2  2  0  2  2  2  0  0  2  0  2  2  2  0  2  0  0  2  2  2  2  0

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

Homogenous weight enumerator: w(x)=1x^0+208x^52+181x^56+62x^60+31x^64+18x^68+11x^72

The gray image is a code over GF(2) with n=112, k=9 and d=52.
This code was found by Heurico 1.16 in 22.4 seconds.