The generator matrix

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

generates a code of length 84 over Z4 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+147x^72+470x^74+663x^76+760x^78+863x^80+954x^82+783x^84+875x^86+742x^88+642x^90+513x^92+395x^94+214x^96+110x^98+33x^100+17x^102+9x^104+1x^110

The gray image is a code over GF(2) with n=168, k=13 and d=72.
This code was found by Heurico 1.10 in 5.12 seconds.