The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+220x^84+158x^88+82x^92+26x^96+10x^100+6x^104+4x^108+1x^112+4x^116

The gray image is a code over GF(2) with n=176, k=9 and d=84.
This code was found by Heurico 1.13 in 60.2 seconds.