The generator matrix

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

generates a code of length 84 over Z4 who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+54x^70+132x^71+249x^72+316x^73+471x^74+530x^75+535x^76+654x^77+675x^78+746x^79+814x^80+844x^81+889x^82+884x^83+907x^84+870x^85+843x^86+880x^87+794x^88+790x^89+692x^90+660x^91+534x^92+406x^93+356x^94+256x^95+221x^96+136x^97+96x^98+70x^99+36x^100+14x^101+20x^102+2x^103+4x^104+2x^105+1x^128

The gray image is a code over GF(2) with n=168, k=14 and d=70.
This code was found by Heurico 1.10 in 19.1 seconds.