The generator matrix

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

generates a code of length 86 over Z4 who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+256x^76+334x^78+451x^80+472x^82+455x^84+476x^86+354x^88+352x^90+279x^92+244x^94+193x^96+96x^98+82x^100+38x^102+9x^104+4x^106

The gray image is a code over GF(2) with n=172, k=12 and d=76.
This code was found by Heurico 1.10 in 3.16 seconds.