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

generates a code of length 81 over Z4 who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+80x^66+335x^68+650x^70+988x^72+1180x^74+1490x^76+1740x^78+1764x^80+1708x^82+1774x^84+1524x^86+1236x^88+840x^90+568x^92+286x^94+145x^96+54x^98+16x^100+2x^104+2x^106+1x^132

The gray image is a code over GF(2) with n=162, k=14 and d=66.
This code was found by Heurico 1.10 in 18 seconds.