The generator matrix

 1  0  0  1  1  1 2X+2  1  1  1  1 3X+2 2X+2  1 3X  1  1  1  1  1  1
 0  1  0  2  3  1  1 2X+2  X 3X+3 3X+1  1 X+2 X+2  1 2X 3X+2  1 3X+3 2X+2  0
 0  0  1 X+3 X+1  2 X+1 3X  1 2X 3X+3  1  1  X  0 2X+3 X+3 3X 3X+2 2X+2 2X+2

generates a code of length 21 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+142x^18+644x^19+760x^20+1156x^21+647x^22+496x^23+167x^24+68x^25+10x^26+4x^27+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 0.047 seconds.