The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+24x^18+5x^20+2x^22

The gray image is a code over GF(2) with n=144, k=5 and d=72.
This code was found by Heurico 1.16 in 6.87e-008 seconds.