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

generates a code of length 81 over Z4 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+254x^68+646x^70+988x^72+1326x^74+1468x^76+1736x^78+1779x^80+1846x^82+1770x^84+1500x^86+1268x^88+840x^90+538x^92+254x^94+123x^96+44x^98+2x^100+1x^128

The gray image is a code over GF(2) with n=162, k=14 and d=68.
This code was found by Heurico 1.10 in 18.5 seconds.