The generator matrix

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

generates a code of length 57 over Z4 who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+26x^43+104x^44+250x^45+371x^46+562x^47+737x^48+850x^49+977x^50+1258x^51+1598x^52+1810x^53+2011x^54+2118x^55+2337x^56+2392x^57+2373x^58+2382x^59+2116x^60+1878x^61+1623x^62+1328x^63+1131x^64+810x^65+555x^66+438x^67+250x^68+174x^69+133x^70+70x^71+41x^72+28x^73+15x^74+8x^75+4x^76+6x^78+2x^79+1x^80

The gray image is a code over GF(2) with n=114, k=15 and d=43.
This code was found by Heurico 1.10 in 44.6 seconds.