The generator matrix

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

generates a code of length 84 over Z4 who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+58x^67+176x^68+352x^69+509x^70+630x^71+826x^72+1128x^73+1328x^74+1588x^75+1986x^76+2334x^77+2608x^78+2848x^79+3216x^80+3348x^81+3705x^82+3994x^83+3806x^84+3868x^85+3828x^86+3746x^87+3438x^88+3072x^89+2694x^90+2230x^91+1985x^92+1592x^93+1276x^94+984x^95+743x^96+536x^97+373x^98+256x^99+175x^100+120x^101+59x^102+48x^103+22x^104+28x^105+4x^106+2x^107+5x^108+6x^109+1x^112+3x^116+1x^128

The gray image is a code over GF(2) with n=168, k=16 and d=67.
This code was found by Heurico 1.10 in 678 seconds.