The generator matrix

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

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+24x^14+98x^15+242x^16+416x^17+514x^18+420x^19+199x^20+80x^21+36x^22+10x^23+5x^24+2x^26+1x^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 0.031 seconds.