The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+116x^51+241x^52+306x^53+463x^54+564x^55+618x^56+700x^57+827x^58+892x^59+913x^60+988x^61+973x^62+1028x^63+1096x^64+1000x^65+981x^66+950x^67+784x^68+718x^69+649x^70+514x^71+393x^72+292x^73+180x^74+90x^75+50x^76+28x^77+22x^78+6x^79+1x^118

The gray image is a code over GF(2) with n=126, k=14 and d=51.
This code was found by Heurico 1.10 in 13.5 seconds.