The generator matrix

 1  1  1  1  1  1  1  1  2
 0  X  0 X+2  0  2 X+2 X+2  2
 0  0  2  0  0  2  2  2  0
 0  0  0  2  2  2  2  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+78x^8+32x^10+16x^12+1x^16

The gray image is a code over GF(2) with n=36, k=7 and d=16.
This code was found by Heurico 1.16 in 0.000371 seconds.