The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  1  1  1  1
 0  1 X+1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  1  0 X^2+X X^2+2 X+2 X+1 X^2+1
 0  0  2  0  0  0  0  2  0  2  2  2  0  0  2  2  0  0
 0  0  0  2  0  0  2  2  0  2  0  2  0  2  2  0  0  2
 0  0  0  0  2  0  2  0  2  2  2  2  0  2  0  2  0  0
 0  0  0  0  0  2  0  2  2  2  0  2  2  2  0  0  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+53x^14+32x^15+578x^16+864x^17+1047x^18+864x^19+567x^20+32x^21+51x^22+5x^24+1x^26+1x^28

The gray image is a code over GF(2) with n=144, k=12 and d=56.
This code was found by Heurico 1.16 in 0.031 seconds.