The generator matrix

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

generates a code of length 89 over Z4 who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+97x^84+116x^86+96x^88+82x^90+41x^92+16x^94+19x^96+18x^98+7x^100+6x^104+4x^106+3x^108+2x^110+2x^112+2x^118

The gray image is a code over GF(2) with n=178, k=9 and d=84.
This code was found by Heurico 1.09 in 0.015 seconds.