The generator matrix

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

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+44x^4+104x^6+128x^7+398x^8+768x^9+272x^10+128x^11+188x^12+8x^14+9x^16

The gray image is a code over GF(2) with n=36, k=11 and d=8.
This code was found by Heurico 1.16 in 0.00411 seconds.