The generator matrix

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

generates a code of length 8 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+47x^4+72x^5+262x^6+312x^7+655x^8+312x^9+276x^10+72x^11+33x^12+6x^14

The gray image is a code over GF(2) with n=32, k=11 and d=8.
This code was found by Heurico 1.16 in 0.00305 seconds.