The generator matrix

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

generates a code of length 70 over Z4 who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+62x^57+173x^58+296x^59+359x^60+476x^61+504x^62+614x^63+698x^64+756x^65+941x^66+874x^67+957x^68+992x^69+945x^70+996x^71+1020x^72+954x^73+847x^74+816x^75+741x^76+576x^77+514x^78+418x^79+251x^80+244x^81+159x^82+78x^83+62x^84+36x^85+13x^86+4x^87+6x^88+1x^116

The gray image is a code over GF(2) with n=140, k=14 and d=57.
This code was found by Heurico 1.10 in 15.3 seconds.