The generator matrix

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

generates a code of length 87 over Z4 who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+60x^84+100x^86+67x^88+4x^90+5x^92+1x^96+4x^98+7x^100+4x^102+2x^104+1x^112

The gray image is a code over GF(2) with n=174, k=8 and d=84.
This code was found by Heurico 1.16 in 0.132 seconds.