The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+89x^82+137x^84+93x^86+65x^88+44x^90+26x^92+11x^94+16x^96+5x^98+5x^100+10x^102+4x^104+2x^108+2x^110+2x^118

The gray image is a code over GF(2) with n=174, k=9 and d=82.
This code was found by Heurico 1.10 in 0.172 seconds.