The generator matrix

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

generates a code of length 84 over Z4 who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+40x^71+84x^72+168x^73+237x^74+304x^75+324x^76+344x^77+449x^78+396x^79+364x^80+402x^81+406x^82+432x^83+417x^84+416x^85+448x^86+430x^87+392x^88+370x^89+329x^90+274x^91+268x^92+258x^93+173x^94+130x^95+118x^96+72x^97+60x^98+38x^99+15x^100+14x^101+10x^102+4x^103+4x^105+1x^112

The gray image is a code over GF(2) with n=168, k=13 and d=71.
This code was found by Heurico 1.10 in 5.05 seconds.