The generator matrix

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

generates a code of length 21 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+28x^17+160x^18+548x^19+744x^20+1170x^21+730x^22+528x^23+141x^24+16x^25+12x^26+12x^27+2x^28+2x^29+2x^30

The gray image is a code over GF(2) with n=168, k=12 and d=68.
This code was found by Heurico 1.16 in 0.063 seconds.