The generator matrix

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

generates a code of length 64 over Z4 who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+44x^51+114x^52+258x^53+329x^54+416x^55+537x^56+626x^57+699x^58+776x^59+869x^60+878x^61+1019x^62+1086x^63+1070x^64+1032x^65+994x^66+956x^67+871x^68+828x^69+760x^70+664x^71+522x^72+340x^73+252x^74+200x^75+110x^76+68x^77+40x^78+18x^79+2x^80+2x^81+2x^82+1x^114

The gray image is a code over GF(2) with n=128, k=14 and d=51.
This code was found by Heurico 1.10 in 13.5 seconds.