The generator matrix

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

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+116x^14+734x^15+1488x^16+3654x^17+4348x^18+3780x^19+1474x^20+628x^21+120x^22+30x^23+5x^24+6x^25

The gray image is a code over GF(2) with n=144, k=14 and d=56.
This code was found by Heurico 1.16 in 0.547 seconds.