The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  2  1  1  1  1  2  1  1  1  1  1  1  1  2  0  0  0  0  1  2  1  1  1  1  1  1  1  1  1  1  1
 0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  2  2  2  2  0  0  2  2  0  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  2  2  2  0  0  0  0  0  2  0  2  2  2  2  2  2  2  2  0  0  0
 0  0  2  0  0  0  2  2  2  2  2  0  2  2  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  2  2  2  2  0  0  0  2  2  0  2  2  0  0  0  0  0  2  2  2  2  0  0  0  2  2  0  0  0  2  2  2  2  0  2  2  2  0  0  0  2  2  2  0  0  2  2  0  0  0  0  2
 0  0  0  2  0  2  2  2  0  0  0  0  2  2  2  2  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  0  0  2  2  0  2  2  0  0  0  2  2  0  0  2  2  2  2  0  0  0  0  2  2  0  2  0  2  2  0  0  2  2  2  0  2  2  0  0  0  0  2  2  0  0  2  2  0  0  2  2
 0  0  0  0  2  2  0  2  2  0  2  2  2  0  0  2  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  0  0  0  2  2  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  2  0  2  0  2  0  2  0  2  0  0  2  0  2  0  2  0  2  2  0  0  2  0  2  2  0  2  0  0  2  0

generates a code of length 86 over Z4 who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+28x^85+13x^86+14x^88+4x^93+1x^94+1x^96+1x^102+1x^110

The gray image is a code over GF(2) with n=172, k=6 and d=85.
This code was found by Heurico 1.16 in 2.84 seconds.