The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+398x^14+1220x^15+3449x^16+7256x^17+8174x^18+7200x^19+3472x^20+1192x^21+354x^22+28x^23+22x^24+2x^26

The gray image is a code over GF(2) with n=144, k=15 and d=56.
This code was found by Heurico 1.16 in 2 seconds.