The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  X  1  X  X  1  X
 0 X^2+2  0  0  2 X^2+2 X^2+2 X^2  0  2 X^2  0 X^2  0 X^2 X^2 X^2 X^2+2 X^2 X^2  2
 0  0 X^2+2  0 X^2+2 X^2+2 X^2  2  0 X^2  0 X^2+2  2  2 X^2+2 X^2 X^2+2 X^2+2  0  2  2
 0  0  0 X^2+2 X^2  2 X^2 X^2  2  2 X^2 X^2  0  2 X^2+2  0  0 X^2  0 X^2+2 X^2+2

generates a code of length 21 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+96x^18+32x^19+114x^20+576x^21+90x^22+32x^23+54x^24+20x^26+6x^28+2x^30+1x^32

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 47.2 seconds.