The generator matrix

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

generates a code of length 56 over Z4 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+81x^44+302x^46+499x^48+786x^50+962x^52+976x^54+1014x^56+1054x^58+921x^60+688x^62+476x^64+248x^66+131x^68+42x^70+10x^72+1x^84

The gray image is a code over GF(2) with n=112, k=13 and d=44.
This code was found by Heurico 1.10 in 2.95 seconds.