The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  2  0  0  0  2  0  0  2  2  0  0  2  2  2  2  0  0  0  0  2
 0  0  2  0  0  2  0  2  2  0  2  2  2  2  0  0  0  0  0  2  2
 0  0  0  2  0  2  2  2  0  0  2  0  0  2  2  2  0  0  2  2  0
 0  0  0  0  2  2  2  0  0  2  2  2  2  0  0  2  0  2  2  0  0

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+5x^18+10x^20+224x^21+10x^22+5x^24+1x^42

The gray image is a code over GF(2) with n=168, k=8 and d=72.
This code was found by Heurico 1.16 in 1.05e-007 seconds.