The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+21x^2+120x^4+336x^6+384x^7+546x^8+5376x^9+546x^10+384x^11+336x^12+120x^14+21x^16+1x^18

The gray image is a code over GF(2) with n=36, k=13 and d=4.
This code was found by Heurico 1.16 in 0.0295 seconds.