The generator matrix

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

generates a code of length 85 over Z4 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+99x^78+194x^80+175x^82+153x^84+114x^86+75x^88+54x^90+42x^92+27x^94+23x^96+29x^98+15x^100+12x^102+7x^104+2x^106+2x^108

The gray image is a code over GF(2) with n=170, k=10 and d=78.
This code was found by Heurico 1.16 in 0.299 seconds.