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

generates a code of length 84 over Z4 who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+48x^82+39x^84+24x^86+7x^88+6x^90+2x^106+1x^108

The gray image is a code over GF(2) with n=168, k=7 and d=82.
This code was found by Heurico 1.16 in 51.9 seconds.