The generator matrix

 1  0  1  1  1 3X+2  1  1  2  1  1  0  1  1  X  1  1  1
 0  1 X+1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  0 3X+2 3X+2 2X+3 X+1  0
 0  0 2X  0  0 2X 2X  0  0 2X 2X 2X  0  0 2X  0  0  0
 0  0  0 2X  0 2X 2X 2X 2X  0 2X  0 2X  0  0 2X 2X  0
 0  0  0  0 2X 2X 2X 2X  0 2X  0 2X  0 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+26x^14+78x^15+189x^16+500x^17+465x^18+496x^19+190x^20+76x^21+20x^22+2x^23+3x^24+1x^26+1x^32

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 0.016 seconds.