The generator matrix

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

generates a code of length 69 over Z4 who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+46x^57+96x^58+196x^59+252x^60+296x^61+347x^62+386x^63+425x^64+424x^65+465x^66+488x^67+515x^68+500x^69+450x^70+444x^71+479x^72+440x^73+400x^74+346x^75+303x^76+258x^77+182x^78+152x^79+116x^80+74x^81+39x^82+34x^83+17x^84+10x^85+4x^86+2x^87+3x^88+1x^92+1x^94

The gray image is a code over GF(2) with n=138, k=13 and d=57.
This code was found by Heurico 1.10 in 7.56 seconds.