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.