The generator matrix
1 1 1 1 X X X X 1
0 X 0 X 0 X X 0 0
0 0 X X X X 0 0 0
0 0 0 X^2 0 0 0 X^2 0
0 0 0 0 X^2 0 0 X^2 0
0 0 0 0 0 X^2 0 X^2 0
0 0 0 0 0 0 X^2 X^2 0
generates a code of length 9 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+45x^4+32x^5+79x^6+320x^7+131x^8+832x^9+131x^10+320x^11+79x^12+32x^13+45x^14+1x^18
The gray image is a linear code over GF(2) with n=36, k=11 and d=8.
This code was found by Heurico 1.16 in 0.00366 seconds.