The generator matrix

 1  0  1  1  1 X+2  1  1 2X+2  1  1 3X  1  1  1  1  1  1  X  X  1
 0  1 X+1 X+2  3  1 2X+2 3X+3  1 3X 2X+1  1  0 X+2 2X+2 3X X+1  3  0  0  0
 0  0 2X  0  0  0  0 2X  0 2X 2X 2X  0  0 2X 2X  0 2X  0  0  0
 0  0  0 2X  0  0 2X 2X  0 2X  0 2X  0 2X 2X  0  0  0 2X 2X  0
 0  0  0  0 2X  0 2X  0 2X 2X 2X 2X  0 2X  0 2X  0  0  0 2X  0
 0  0  0  0  0 2X  0 2X 2X 2X  0 2X 2X 2X  0  0 2X  0  0  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+43x^16+54x^17+136x^18+430x^19+990x^20+812x^21+964x^22+460x^23+108x^24+30x^25+48x^26+6x^27+10x^28+4x^30

The gray image is a code over GF(2) with n=168, k=12 and d=64.
This code was found by Heurico 1.16 in 0.047 seconds.