The generator matrix

 1  0  0  0  1  1  1  1  1
 0  1  0  0  X  3  1 X+1  2
 0  0  1  0 X+1  1  X  1  0
 0  0  0  1  1  X X+1  1  X

generates a code of length 9 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+36x^5+148x^6+432x^7+878x^8+1112x^9+872x^10+432x^11+144x^12+36x^13+4x^14+1x^16

The gray image is a code over GF(2) with n=36, k=12 and d=10.
This code was found by Heurico 1.16 in 0.019 seconds.