The generator matrix
1 0 1 1 1 2 X 1 1
0 1 1 0 1 1 X+2 X+1 0
0 0 X 0 0 2 X 0 0
0 0 0 X 0 X+2 0 2 0
0 0 0 0 X 2 X 2 0
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+24x^4+86x^5+157x^6+444x^7+875x^8+964x^9+778x^10+496x^11+186x^12+54x^13+25x^14+4x^15+2x^16
The gray image is a code over GF(2) with n=36, k=12 and d=8.
This code was found by Heurico 1.16 in 0.0105 seconds.