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  1  1
 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  2  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  2  2
 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  0  0

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

Homogenous weight enumerator: w(x)=1x^0+14x^86+32x^87+14x^88+2x^94+1x^96

The gray image is a code over GF(2) with n=172, k=6 and d=86.
This code was found by Heurico 1.16 in 0.118 seconds.