The generator matrix

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

generates a code of length 18 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+390x^14+1306x^15+3445x^16+6792x^17+8754x^18+7110x^19+3368x^20+1144x^21+418x^22+30x^23+2x^24+6x^26+2x^27

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 1.92 seconds.