The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+244x^54+405x^56+462x^58+533x^60+482x^62+509x^64+424x^66+393x^68+286x^70+188x^72+102x^74+48x^76+16x^78+1x^80+2x^84

The gray image is a code over GF(2) with n=126, k=12 and d=54.
This code was found by Heurico 1.16 in 95.5 seconds.