The generator matrix
1 0 1 1 1 X^2+X 1 1 1
0 1 X+1 X^2+X 1 1 0 0 X^2+X
0 0 X^2 0 0 X^2 X^2 X^2 0
0 0 0 X^2 0 X^2 X^2 0 0
0 0 0 0 X^2 X^2 X^2 X^2 X^2
generates a code of length 9 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+22x^6+32x^7+170x^8+64x^9+168x^10+32x^11+20x^12+2x^14+1x^16
The gray image is a linear code over GF(2) with n=36, k=9 and d=12.
This code was found by Heurico 1.16 in 0.000842 seconds.