The generator matrix
1 1 1 1 1 1 1 1 X X 1 X X 1 X^2 0 1 1 X^2 X^2 1
0 X^2+2 2 X^2 0 X^2+2 2 X^2 X^2+2 X^2 0 2 0 X^2+2 X^2+2 X^2 2 X^2 2 0 0
generates a code of length 21 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 20.
Homogenous weight enumerator: w(x)=1x^0+19x^20+16x^21+19x^22+8x^23+1x^26
The gray image is a code over GF(2) with n=168, k=6 and d=80.
This code was found by Heurico 1.16 in -6.48e-008 seconds.