The generator matrix

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

generates a code of length 57 over Z4 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+78x^42+84x^43+389x^44+436x^45+810x^46+1034x^47+1383x^48+1600x^49+2211x^50+2540x^51+2989x^52+3538x^53+3829x^54+4662x^55+4518x^56+4756x^57+4589x^58+4792x^59+4133x^60+3778x^61+3281x^62+2574x^63+2164x^64+1592x^65+1210x^66+836x^67+667x^68+374x^69+319x^70+114x^71+132x^72+52x^73+47x^74+4x^75+6x^76+2x^77+9x^78+2x^80+1x^82

The gray image is a code over GF(2) with n=114, k=16 and d=42.
This code was found by Heurico 1.10 in 309 seconds.