The generator matrix

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

generates a code of length 82 over Z4 who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+2x^86+8x^87+3x^88+2x^90

The gray image is a code over GF(2) with n=164, k=4 and d=86.
This code was found by Heurico 1.16 in 0.119 seconds.