The generator matrix

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

generates a code of length 62 over Z4 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+125x^54+319x^56+307x^58+242x^60+240x^62+209x^64+184x^66+166x^68+111x^70+77x^72+45x^74+8x^76+12x^78+2x^80

The gray image is a code over GF(2) with n=124, k=11 and d=54.
This code was found by Heurico 1.10 in 0.187 seconds.