The generator matrix

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

generates a code of length 55 over Z4 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+29x^56+1x^64+1x^72

The gray image is a code over GF(2) with n=110, k=5 and d=56.
This code was found by Heurico 1.16 in 0.0321 seconds.