The generator matrix

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

generates a code of length 83 over Z4 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+26x^68+70x^69+166x^70+212x^71+376x^72+450x^73+507x^74+552x^75+576x^76+654x^77+712x^78+844x^79+784x^80+866x^81+908x^82+874x^83+966x^84+912x^85+802x^86+880x^87+778x^88+680x^89+621x^90+530x^91+434x^92+360x^93+297x^94+146x^95+133x^96+92x^97+76x^98+52x^99+22x^100+12x^101+6x^102+6x^103+1x^126

The gray image is a code over GF(2) with n=166, k=14 and d=68.
This code was found by Heurico 1.10 in 18.6 seconds.