The generator matrix

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

generates a code of length 9 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+3x^8+22x^9+4x^10+2x^13

The gray image is a code over GF(2) with n=36, k=5 and d=16.
This code was found by Heurico 1.16 in 0.000187 seconds.