The generator matrix

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

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+394x^14+1252x^15+3413x^16+7208x^17+8246x^18+7216x^19+3448x^20+1176x^21+350x^22+44x^23+18x^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 2.11 seconds.