The generator matrix

 1  0  1  1  1  2 X^2+X  1  1 X^2+X+2  1  1  1  X  1  1  1  1 X+2  1  X
 0  1 X+1 X^2+X+2 X^2+1  1  1  2 X^2+X  1  3 X^2+X+1 X^2+3 X+2 X+1 X^2+X+3  3 X^2  1 X^2+2  1
 0  0 X^2 X^2+2  2 X^2  0 X^2  0 X^2+2  2 X^2+2 X^2 X^2+2  0  2 X^2 X^2+2  2  2 X^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+184x^19+192x^20+360x^21+88x^22+136x^23+37x^24+24x^25+2x^28

The gray image is a code over GF(2) with n=168, k=10 and d=76.
This code was found by Heurico 1.16 in 0.015 seconds.