The generator matrix

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

generates a code of length 67 over Z4 who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+66x^57+124x^58+176x^59+205x^60+226x^61+239x^62+244x^63+242x^64+242x^65+257x^66+244x^67+255x^68+236x^69+218x^70+164x^71+184x^72+174x^73+117x^74+132x^75+104x^76+66x^77+66x^78+56x^79+32x^80+14x^81+2x^82+8x^83+1x^86+1x^88

The gray image is a code over GF(2) with n=134, k=12 and d=57.
This code was found by Heurico 1.10 in 0.843 seconds.