The generator matrix

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

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+636x^14+2424x^15+6902x^16+13816x^17+17796x^18+14136x^19+6966x^20+2184x^21+568x^22+80x^23+27x^24

The gray image is a code over GF(2) with n=144, k=16 and d=56.
This code was found by Heurico 1.16 in 7.41 seconds.