The generator matrix

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

generates a code of length 18 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+51x^14+48x^15+293x^16+272x^17+733x^18+272x^19+274x^20+48x^21+45x^22+6x^24+3x^26+2x^28

The gray image is a code over GF(2) with n=144, k=11 and d=56.
This code was found by Heurico 1.16 in 0.032 seconds.