The generator matrix
1 0 1 1 X^2+X 1 1 1 0 1 1 X 1 1 X+2 1 1 1 X^2 X^2+2 1
0 1 1 X^2+X 1 X+3 X^2+3 X^2 1 X X^2+X+3 1 X^2 1 1 X^2+X+1 X+2 X 1 X X+2
0 0 X 0 2 X^2 X^2+2 X+2 X^2+X+2 X X^2+X+2 X+2 X^2+X+2 X^2+X X^2+X X X^2+X+2 X^2 X^2+2 X^2+X+2 0
0 0 0 2 2 0 2 0 2 2 2 0 0 0 2 0 0 0 2 2 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+212x^18+512x^19+904x^20+944x^21+849x^22+424x^23+177x^24+32x^25+26x^26+8x^27+6x^28+1x^30
The gray image is a code over GF(2) with n=168, k=12 and d=72.
This code was found by Heurico 1.16 in 0.109 seconds.