The generator matrix

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

generates a code of length 88 over Z4 who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+68x^84+50x^86+47x^88+28x^90+32x^92+18x^94+10x^96+1x^104+1x^160

The gray image is a code over GF(2) with n=176, k=8 and d=84.
This code was found by Heurico 1.16 in 0.184 seconds.