The generator matrix

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

generates a code of length 71 over Z4 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+80x^56+92x^57+330x^58+356x^59+563x^60+638x^61+847x^62+930x^63+1089x^64+1284x^65+1433x^66+1722x^67+1843x^68+2056x^69+1976x^70+2148x^71+2020x^72+2018x^73+1776x^74+1842x^75+1562x^76+1474x^77+1244x^78+886x^79+735x^80+508x^81+478x^82+266x^83+235x^84+104x^85+76x^86+36x^87+58x^88+18x^89+30x^90+6x^91+5x^92+1x^94+1x^96+1x^98

The gray image is a code over GF(2) with n=142, k=15 and d=56.
This code was found by Heurico 1.10 in 118 seconds.