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

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

Homogenous weight enumerator: w(x)=1x^0+207x^76+382x^78+501x^80+430x^82+475x^84+410x^86+410x^88+336x^90+293x^92+204x^94+210x^96+120x^98+63x^100+36x^102+14x^104+2x^106+2x^108

The gray image is a code over GF(2) with n=172, k=12 and d=76.
This code was found by Heurico 1.16 in 7.82 seconds.