The generator matrix

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

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+52x^4+144x^5+404x^6+2112x^7+2634x^8+5728x^9+2568x^10+2112x^11+444x^12+144x^13+36x^14+5x^16

The gray image is a code over GF(2) with n=36, k=14 and d=8.
This code was found by Heurico 1.16 in 0.145 seconds.