The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+28x^54+42x^55+56x^56+70x^57+47x^58+50x^59+37x^60+22x^61+27x^62+20x^63+12x^64+22x^65+12x^66+12x^67+18x^68+10x^69+8x^70+2x^71+2x^72+4x^73+5x^74+2x^75+1x^76+1x^78+1x^80

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 0.0658 seconds.