The generator matrix

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

generates a code of length 21 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+20x^19+17x^20+184x^21+8x^22+20x^23+5x^24+1x^36

The gray image is a code over GF(2) with n=168, k=8 and d=76.
This code was found by Heurico 1.16 in 0.016 seconds.