The generator matrix

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

generates a code of length 60 over Z4 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+156x^54+192x^56+178x^58+147x^60+84x^62+90x^64+52x^66+51x^68+32x^70+23x^72+10x^74+6x^76+2x^80

The gray image is a code over GF(2) with n=120, k=10 and d=54.
This code was found by Heurico 1.10 in 4.39 seconds.