The generator matrix

 1  0  1  1  1 X+2  1  1  X  1  1 3X+2  1  1  2  1  1  1  1  1  1
 0  1 X+1 3X+2 2X+3  1 3X+3 X+2  1  X X+1  1  2 2X+1  1 2X 2X 3X+2 X+1 2X+2 3X+2
 0  0 2X+2  0 2X 2X+2  2 2X+2  2  2 2X  0  0 2X  0 2X+2 2X+2 2X  0  2 2X+2
 0  0  0 2X 2X  0 2X 2X 2X  0  0 2X 2X  0 2X  0 2X  0 2X 2X  0

generates a code of length 21 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+89x^18+212x^19+618x^20+224x^21+611x^22+200x^23+82x^24+3x^26+4x^27+2x^28+1x^30+1x^32

The gray image is a code over GF(2) with n=168, k=11 and d=72.
This code was found by Heurico 1.16 in 0.031 seconds.