The generator matrix

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

generates a code of length 84 over Z4 who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+56x^75+97x^76+140x^77+133x^78+156x^79+144x^80+112x^81+164x^82+114x^83+104x^84+92x^85+99x^86+74x^87+57x^88+84x^89+59x^90+58x^91+64x^92+52x^93+42x^94+42x^95+24x^96+20x^97+13x^98+12x^99+19x^100+12x^101+2x^102+2x^104

The gray image is a code over GF(2) with n=168, k=11 and d=75.
This code was found by Heurico 1.10 in 0.281 seconds.