The generator matrix

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

generates a code of length 56 over Z4 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+61x^42+70x^43+293x^44+366x^45+556x^46+694x^47+908x^48+1072x^49+1317x^50+1464x^51+1684x^52+1996x^53+2224x^54+2446x^55+2220x^56+2466x^57+2185x^58+2146x^59+1944x^60+1664x^61+1282x^62+1040x^63+887x^64+526x^65+452x^66+290x^67+220x^68+94x^69+104x^70+36x^71+32x^72+8x^73+8x^74+6x^75+3x^76+2x^78+1x^82

The gray image is a code over GF(2) with n=112, k=15 and d=42.
This code was found by Heurico 1.10 in 43.2 seconds.