The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1  1  1 2X  1  1  1  1
 0  1 X+1 X+2 2X+3  1 2X+3 3X+2  1  0 3X+1  X  2  1  3 X+1 3X+2 2X
 0  0 2X+2  0  0 2X  2 2X+2 2X+2  2  0 2X 2X 2X+2  0  2  0 2X+2
 0  0  0  2 2X 2X+2  2 2X+2 2X+2 2X+2 2X+2 2X+2  0 2X 2X+2 2X+2  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+30x^14+120x^15+442x^16+904x^17+1124x^18+904x^19+407x^20+120x^21+30x^22+13x^24+1x^28

The gray image is a code over GF(2) with n=144, k=12 and d=56.
This code was found by Heurico 1.16 in 0.047 seconds.