The generator matrix

 1  0  0  1  1  1  0  X  1 3X 3X+2  1  1  1 3X+2  1  1 2X 2X+2 2X  1
 0  1  0  X  1 3X+3  1 3X+2 3X  1  1 2X+1 X+1  X  0  X 3X+3 3X+2  1 X+2  0
 0  0  1  1 2X+3  X 3X+3  1 3X+3 2X+2 X+1 3X+1  2  1  1 2X+2 X+1  1 X+3  1 3X+3
 0  0  0 2X+2  2 2X 2X+2  2  2 2X+2  0 2X 2X+2  0 2X 2X  2 2X  0  2 2X+2

generates a code of length 21 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+146x^17+921x^18+1724x^19+3313x^20+4144x^21+3499x^22+1584x^23+811x^24+204x^25+27x^26+4x^27+3x^28+1x^30+2x^33

The gray image is a code over GF(2) with n=168, k=14 and d=68.
This code was found by Heurico 1.16 in 0.688 seconds.