The generator matrix

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

generates a code of length 63 over Z4 who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+22x^51+107x^52+192x^53+252x^54+256x^55+335x^56+392x^57+431x^58+408x^59+467x^60+526x^61+481x^62+514x^63+467x^64+512x^65+479x^66+446x^67+435x^68+396x^69+268x^70+220x^71+185x^72+136x^73+121x^74+52x^75+47x^76+22x^77+15x^78+2x^79+4x^80+1x^98

The gray image is a code over GF(2) with n=126, k=13 and d=51.
This code was found by Heurico 1.10 in 3.5 seconds.