The generator matrix

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

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+80x^5+296x^6+864x^7+1742x^8+2208x^9+1776x^10+864x^11+272x^12+80x^13+8x^14+1x^16

The gray image is a code over GF(2) with n=36, k=13 and d=10.
This code was found by Heurico 1.13 in 0.0157 seconds.