The generator matrix

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

generates a code of length 83 over Z4 who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+16x^67+119x^68+226x^69+349x^70+490x^71+608x^72+758x^73+872x^74+1048x^75+1251x^76+1380x^77+1370x^78+1608x^79+1694x^80+1668x^81+1748x^82+1888x^83+2075x^84+1864x^85+1773x^86+1608x^87+1516x^88+1392x^89+1158x^90+1080x^91+857x^92+652x^93+508x^94+352x^95+277x^96+204x^97+132x^98+96x^99+39x^100+38x^101+24x^102+6x^103+8x^104+10x^105+2x^106+2x^108+1x^116

The gray image is a code over GF(2) with n=166, k=15 and d=67.
This code was found by Heurico 1.10 in 157 seconds.