The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+45x^54+76x^55+118x^56+134x^57+122x^58+150x^59+128x^60+130x^61+131x^62+128x^63+122x^64+120x^65+107x^66+96x^67+81x^68+66x^69+62x^70+44x^71+49x^72+48x^73+39x^74+18x^75+11x^76+12x^77+6x^78+2x^80+2x^81

The gray image is a code over GF(2) with n=126, k=11 and d=54.
This code was found by Heurico 1.10 in 0.187 seconds.