The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1
0 X 2X+2 X+2 0 X+2 2X+2 3X 0 X+2 2X+2 3X 0 2X 3X+2 3X X+2 2X+2 0 3X 2X
0 0 2X 0 0 0 2X 2X 2X 0 0 2X 0 2X 0 0 2X 2X 2X 0 0
0 0 0 2X 0 0 2X 2X 0 2X 2X 2X 2X 2X 0 0 0 2X 2X 2X 2X
0 0 0 0 2X 2X 0 0 2X 2X 2X 2X 0 2X 0 2X 2X 2X 0 0 2X
generates a code of length 21 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 18.
Homogenous weight enumerator: w(x)=1x^0+89x^18+106x^20+640x^21+114x^22+52x^24+21x^26+1x^40
The gray image is a code over GF(2) with n=168, k=10 and d=72.
This code was found by Heurico 1.16 in 0.031 seconds.