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

generates a code of length 83 over Z4 who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+18x^84+8x^86+4x^88+1x^104

The gray image is a code over GF(2) with n=166, k=5 and d=84.
This code was found by Heurico 1.16 in 0.102 seconds.