The generator matrix

 1  0  0  1  1  1  X  X  1
 0  1  0  1 X+2 X+3  1  0  0
 0  0  1  1 X+3 X+2  1  0  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  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+61x^4+160x^5+255x^6+1280x^7+707x^8+3264x^9+707x^10+1280x^11+255x^12+160x^13+61x^14+1x^18

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 0.0339 seconds.