The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+84x^54+57x^56+115x^58+24x^60+106x^62+37x^64+72x^66+2x^70+7x^72+5x^74+2x^88

The gray image is a code over GF(2) with n=120, k=9 and d=54.
This code was found by Heurico 1.16 in 2.98 seconds.