The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  1  1  1  1  1
 0  2  0  0  0  0  0  0  2  0  2  2  0  2  2  0  0  2  2  0  0
 0  0  2  0  0  0  0  0  2  2  2  0  2  2  0  0  2  2  0  0  0
 0  0  0  2  0  0  0  2  0  2  0  2  2  2  0  0  0  2  2  0  0
 0  0  0  0  2  0  0  2  0  0  2  2  2  0  2  0  2  2  0  0  0
 0  0  0  0  0  2  0  2  2  0  2  0  0  2  2  2  2  0  0  0  0
 0  0  0  0  0  0  2  2  2  0  0  2  2  0  2  2  0  0  2  0  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+45x^16+129x^20+768x^21+50x^24+30x^28+1x^36

The gray image is a code over GF(2) with n=168, k=10 and d=64.
This code was found by Heurico 1.16 in 0 seconds.