The generator matrix

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

generates a code of length 21 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+56x^16+130x^18+144x^19+469x^20+496x^21+428x^22+112x^23+135x^24+16x^25+50x^26+11x^28

The gray image is a code over GF(2) with n=168, k=11 and d=64.
This code was found by Heurico 1.16 in 0.031 seconds.