The generator matrix

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

generates a code of length 63 over Z4 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+250x^54+392x^56+516x^58+472x^60+478x^62+484x^64+470x^66+398x^68+278x^70+196x^72+108x^74+34x^76+10x^78+7x^80+2x^82

The gray image is a code over GF(2) with n=126, k=12 and d=54.
This code was found by Heurico 1.10 in 149 seconds.