The generator matrix
1 1 1 1 1 1 1 1 1 X 1 1 1 X 1 1 1 1 X X X
0 2X+2 0 2X+2 0 2X+2 0 2 2X 2X+2 0 0 0 2X+2 2X 2X+2 2X+2 2X 0 2X 0
0 0 2X 0 0 0 0 0 2X 0 2X 2X 0 0 2X 0 2X 2X 0 0 2X
0 0 0 2X 0 0 0 2X 0 0 2X 2X 2X 0 0 2X 2X 2X 2X 2X 2X
0 0 0 0 2X 0 0 0 0 2X 2X 2X 0 2X 2X 2X 2X 0 0 0 0
0 0 0 0 0 2X 0 2X 0 2X 2X 0 2X 0 2X 0 2X 2X 0 0 0
0 0 0 0 0 0 2X 0 2X 2X 0 2X 2X 2X 0 2X 0 0 2X 2X 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+64x^16+87x^18+64x^19+110x^20+1408x^21+110x^22+64x^23+78x^24+48x^26+2x^28+10x^30+1x^32+1x^34
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.