The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+33x^84+24x^86+3x^88+3x^92

The gray image is a code over GF(2) with n=168, k=6 and d=84.
This code was found by Heurico 1.16 in 0.128 seconds.