The generator matrix

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

generates a code of length 87 over Z4 who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+94x^82+114x^84+114x^86+65x^88+44x^90+21x^92+18x^94+8x^96+10x^98+5x^100+4x^102+8x^104+2x^106+2x^112+2x^114

The gray image is a code over GF(2) with n=174, k=9 and d=82.
This code was found by Heurico 1.16 in 20.9 seconds.