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

generates a code of length 18 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+76x^17+101x^18+76x^19+1x^26+1x^28

The gray image is a code over GF(2) with n=144, k=8 and d=68.
This code was found by Heurico 1.16 in 3.62e-008 seconds.