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

generates a code of length 79 over Z4 who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+14x^84+1x^88

The gray image is a code over GF(2) with n=158, k=4 and d=84.
This code was found by Heurico 1.16 in 0.0979 seconds.