The generator matrix

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

generates a code of length 84 over Z4 who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+44x^77+89x^78+102x^79+105x^80+88x^81+98x^82+70x^83+58x^84+56x^85+36x^86+38x^87+26x^88+44x^89+28x^90+22x^91+12x^92+14x^93+21x^94+18x^95+12x^96+2x^97+12x^98+2x^99+6x^100+6x^101+2x^102+2x^103+2x^104+2x^105+2x^106+2x^107+2x^112

The gray image is a code over GF(2) with n=168, k=10 and d=77.
This code was found by Heurico 1.16 in 0.545 seconds.