The generator matrix

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

generates a code of length 55 over Z4 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+106x^52+24x^54+82x^56+8x^58+17x^60+8x^64+9x^68+1x^72

The gray image is a code over GF(2) with n=110, k=8 and d=52.
This code was found by Heurico 1.16 in 0.0891 seconds.