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

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

Homogenous weight enumerator: w(x)=1x^0+30x^84+64x^86+30x^88+1x^96+1x^108+1x^140

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 0.155 seconds.