The generator matrix

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

generates a code of length 21 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+64x^16+87x^18+64x^19+110x^20+1408x^21+110x^22+64x^23+78x^24+48x^26+2x^28+10x^30+1x^32+1x^34

The gray image is a code over GF(2) with n=168, k=11 and d=64.
This code was found by Heurico 1.16 in 0.032 seconds.