The generator matrix

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

generates a code of length 8 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+16x^5+41x^6+144x^7+109x^8+144x^9+38x^10+16x^11+2x^12+1x^14

The gray image is a code over GF(2) with n=32, k=9 and d=10.
This code was found by Heurico 1.16 in 0.000702 seconds.