The generator matrix

 1  0  0  0  0  1  1  1  2  1  1  1  2  0  1  0  0  1  1  2  1  0  0  2  1  1  2  1  1  1  2  0  1  1  1  1  2  2  2  1  0  1  0  1  0  1  0  1  1  1  1  0  2  1  0  2  2  0  0  1  2  0  2  1  0  2  2  0  2  1  1  0  1  0  1  1  2  0  2  1  1  1  0  0  0  2
 0  1  0  0  0  0  0  2  0  1  1  1  1  1  1  1  2  1  1  1  3  0  2  1  2  3  1  0  0  2  0  1  2  3  0  2  0  1  1  2  0  3  1  0  2  3  1  0  0  3  1  2  1  1  0  1  1  1  1  0  2  0  2  3  1  0  1  2  2  1  1  2  0  0  1  0  2  2  2  0  1  3  1  0  2  2
 0  0  1  0  0  0  0  0  2  0  2  0  2  2  2  0  2  1  1  3  1  1  1  1  3  3  3  1  3  1  1  3  0  3  1  2  1  1  0  0  2  2  2  1  1  0  1  2  3  3  2  2  0  3  1  2  2  3  1  1  1  0  1  1  1  1  3  0  0  0  1  1  2  2  3  3  0  2  2  2  1  0  3  0  1  1
 0  0  0  1  0  0  1  1  1  1  0  3  1  2  2  1  0  3  2  2  0  0  1  0  2  1  3  3  3  0  1  3  3  2  2  3  3  0  2  0  1  0  2  1  2  0  3  2  1  3  3  1  1  0  3  1  2  1  1  0  3  2  3  1  2  2  2  1  1  1  1  1  3  0  1  0  1  1  0  0  0  3  0  1  0  2
 0  0  0  0  1  1  3  0  3  2  2  3  0  1  3  3  1  1  0  3  3  1  2  2  1  2  1  2  1  2  1  0  0  1  0  1  1  2  2  1  0  3  1  2  1  2  1  2  1  2  2  1  3  2  2  0  2  2  0  0  1  1  3  3  1  1  1  3  2  1  3  2  1  1  0  1  0  3  1  2  1  0  2  1  2  2
 0  0  0  0  0  2  2  0  2  0  0  2  0  2  2  2  2  2  0  2  2  2  0  0  2  0  2  0  2  0  2  2  2  0  2  0  0  2  2  0  2  0  0  2  0  2  0  2  0  2  2  0  0  2  2  2  2  0  2  2  0  0  2  0  2  2  0  0  2  0  2  2  0  0  0  0  0  2  0  2  0  2  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+48x^77+96x^78+136x^79+153x^80+152x^81+178x^82+134x^83+98x^84+116x^85+90x^86+102x^87+93x^88+76x^89+88x^90+62x^91+75x^92+74x^93+38x^94+44x^95+39x^96+34x^97+42x^98+16x^99+19x^100+10x^101+12x^102+12x^103+2x^104+2x^105+4x^107+2x^111

The gray image is a code over GF(2) with n=172, k=11 and d=77.
This code was found by Heurico 1.16 in 0.853 seconds.