The generator matrix

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

generates a code of length 18 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+15x^16+96x^18+15x^20+1x^36

The gray image is a code over GF(2) with n=72, k=7 and d=32.
This code was found by Heurico 1.16 in 0.00146 seconds.