The generator matrix

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

generates a code of length 9 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+76x^4+456x^6+384x^7+2574x^8+1280x^9+2448x^10+384x^11+540x^12+40x^14+9x^16

The gray image is a code over GF(2) with n=36, k=13 and d=8.
This code was found by Heurico 1.16 in 0.0465 seconds.