The generator matrix

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

generates a code of length 83 over Z4 who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+90x^71+157x^72+210x^73+320x^74+348x^75+328x^76+406x^77+454x^78+412x^79+432x^80+406x^81+407x^82+418x^83+427x^84+440x^85+400x^86+400x^87+383x^88+362x^89+290x^90+246x^91+222x^92+160x^93+146x^94+114x^95+90x^96+52x^97+31x^98+20x^99+7x^100+10x^101+2x^105+1x^112

The gray image is a code over GF(2) with n=166, k=13 and d=71.
This code was found by Heurico 1.10 in 5.02 seconds.