The generator matrix

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

generates a code of length 62 over Z4 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+156x^56+182x^58+203x^60+132x^62+95x^64+68x^66+78x^68+36x^70+28x^72+18x^74+15x^76+8x^78+4x^82

The gray image is a code over GF(2) with n=124, k=10 and d=56.
This code was found by Heurico 1.10 in 0.391 seconds.