The generator matrix

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

generates a code of length 86 over Z4 who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+17x^84+36x^85+24x^86+24x^87+11x^88+4x^89+6x^90+1x^96+1x^100+2x^102+1x^104

The gray image is a code over GF(2) with n=172, k=7 and d=84.
This code was found by Heurico 1.16 in 0.129 seconds.