The generator matrix

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

generates a code of length 60 over Z4 who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+28x^45+73x^46+160x^47+291x^48+452x^49+568x^50+694x^51+908x^52+1106x^53+1288x^54+1460x^55+1697x^56+2030x^57+2135x^58+2154x^59+2302x^60+2242x^61+2150x^62+2106x^63+1913x^64+1738x^65+1394x^66+994x^67+862x^68+662x^69+484x^70+320x^71+181x^72+162x^73+87x^74+46x^75+30x^76+26x^77+13x^78+2x^79+5x^80+2x^81+2x^84

The gray image is a code over GF(2) with n=120, k=15 and d=45.
This code was found by Heurico 1.10 in 96.4 seconds.