The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+85x^80+104x^84+45x^88+16x^92+4x^96+1x^152

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 0.124 seconds.