The generator matrix

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

generates a code of length 84 over Z4 who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+62x^80+66x^82+58x^84+20x^86+16x^88+10x^90+14x^92+1x^96+2x^100+2x^104+2x^108+2x^112

The gray image is a code over GF(2) with n=168, k=8 and d=80.
This code was found by Heurico 1.16 in 0.121 seconds.