The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^2  X  X  1
 0 X^2+2  0 X^2+2  0 X^2+2  2 X^2  0 X^2+2  2 X^2  2 X^2  2 X^2 X^2+2 X^2+2  0  0  0
 0  0  2  0  0  2  2  2  2  2  2  0  0  2  0  0  0  0  2  0  0
 0  0  0  2  2  2  2  0  2  0  0  2  2  2  0  0  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+7x^18+2x^19+78x^20+78x^21+72x^22+14x^23+1x^24+2x^25+1x^34

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 3.62e-008 seconds.