The generator matrix

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

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+680x^14+2416x^15+6696x^16+14080x^17+17572x^18+14416x^19+6828x^20+2144x^21+588x^22+96x^23+17x^24+2x^28

The gray image is a code over GF(2) with n=144, k=16 and d=56.
This code was found by Heurico 1.16 in 7.92 seconds.