The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+39x^44+98x^45+197x^46+294x^47+396x^48+484x^49+592x^50+738x^51+754x^52+808x^53+942x^54+1040x^55+1180x^56+1192x^57+1115x^58+1112x^59+1008x^60+926x^61+826x^62+684x^63+534x^64+436x^65+364x^66+244x^67+161x^68+80x^69+55x^70+46x^71+21x^72+8x^73+4x^74+2x^75+2x^76+1x^82

The gray image is a code over GF(2) with n=114, k=14 and d=44.
This code was found by Heurico 1.10 in 11.4 seconds.