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.