The generator matrix
1 1 1 1 1 1 1 1 1 1 X X 2 1 2X 1 1 2X+2 2 1 1
0 X 0 X 0 2X X+2 2 X+2 2 2 X+2 X 2 X 2X+2 X X 0 2 0
0 0 X X 2X+2 3X+2 X+2 2X+2 2X 0 X 0 X X 2 3X+2 3X 3X+2 2X+2 2X+2 2X
0 0 0 2X 0 0 0 2X 2X 2X 0 0 2X 2X 0 0 2X 0 2X 2X 2X
0 0 0 0 2X 2X 0 0 2X 2X 0 2X 2X 0 0 2X 2X 0 0 2X 0
generates a code of length 21 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 17.
Homogenous weight enumerator: w(x)=1x^0+140x^17+228x^18+472x^19+679x^20+1076x^21+666x^22+504x^23+195x^24+92x^25+16x^26+16x^27+5x^28+4x^29+2x^30
The gray image is a code over GF(2) with n=168, k=12 and d=68.
This code was found by Heurico 1.16 in 2.08 seconds.