The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X 1
0 2X 0 0 0 0 0 0 0 0 2X 2X 0 0 0 2X 2X 2X 2X 2X 0
0 0 2X 0 0 0 0 0 0 2X 2X 2X 0 2X 2X 0 2X 2X 0 0 0
0 0 0 2X 0 0 0 0 0 2X 0 2X 2X 2X 0 2X 0 2X 2X 0 0
0 0 0 0 2X 0 0 0 2X 0 0 2X 2X 0 2X 2X 0 0 2X 2X 0
0 0 0 0 0 2X 0 0 2X 0 2X 0 0 2X 2X 2X 0 2X 2X 0 0
0 0 0 0 0 0 2X 0 2X 2X 2X 0 0 0 2X 2X 2X 0 0 2X 0
0 0 0 0 0 0 0 2X 2X 2X 0 0 2X 2X 2X 0 2X 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+78x^16+32x^17+52x^18+1728x^21+48x^24+32x^25+72x^26+1x^32+4x^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 0.047 seconds.