The generator matrix

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

generates a code of length 57 over Z4 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+227x^44+780x^46+1442x^48+2236x^50+3039x^52+3718x^54+4771x^56+4762x^58+4227x^60+3208x^62+2240x^64+1142x^66+581x^68+258x^70+105x^72+18x^74+6x^76+4x^78+1x^80+2x^82

The gray image is a code over GF(2) with n=114, k=15 and d=44.
This code was found by Heurico 1.10 in 45.7 seconds.