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

generates a code of length 82 over Z4 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+63x^68+156x^69+244x^70+290x^71+429x^72+518x^73+639x^74+592x^75+667x^76+812x^77+772x^78+834x^79+894x^80+898x^81+835x^82+862x^83+832x^84+966x^85+829x^86+736x^87+727x^88+664x^89+523x^90+374x^91+361x^92+278x^93+216x^94+132x^95+101x^96+56x^97+35x^98+20x^99+21x^100+4x^101+2x^102+1x^134

The gray image is a code over GF(2) with n=164, k=14 and d=68.
This code was found by Heurico 1.10 in 18.5 seconds.