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

generates a code of length 86 over Z4 who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+54x^77+109x^78+136x^79+107x^80+146x^81+174x^82+124x^83+135x^84+134x^85+129x^86+76x^87+90x^88+90x^89+60x^90+82x^91+62x^92+48x^93+45x^94+64x^95+34x^96+20x^97+44x^98+16x^99+11x^100+12x^101+13x^102+12x^103+8x^104+8x^105+2x^106+2x^107

The gray image is a code over GF(2) with n=172, k=11 and d=77.
This code was found by Heurico 1.10 in 0.281 seconds.