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  1  1  1
 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 X^2+3 X^2  1 X^2+2 X+3
 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+2 X^2+2  0  2 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+176x^19+209x^20+320x^21+152x^22+112x^23+20x^24+32x^25+1x^28+1x^32

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 0.016 seconds.