The generator matrix

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

generates a code of length 86 over Z4 who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+50x^79+117x^80+94x^81+58x^82+102x^83+116x^84+76x^85+20x^86+48x^87+68x^88+34x^89+26x^90+36x^91+38x^92+18x^93+10x^94+10x^95+26x^96+14x^97+12x^98+6x^99+14x^100+14x^101+2x^102+4x^103+4x^104+2x^105+2x^109+2x^117

The gray image is a code over GF(2) with n=172, k=10 and d=79.
This code was found by Heurico 1.16 in 8.09 seconds.