The generator matrix
1 0 0 0 0 1 X^2+X 1 1
0 1 0 0 0 0 1 X X^2
0 0 1 0 0 X 1 X+1 X^2+1
0 0 0 1 0 X+1 0 1 1
0 0 0 0 1 1 X 0 X^2
0 0 0 0 0 X^2 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+119x^4+516x^5+2446x^6+6388x^7+14851x^8+16904x^9+14820x^10+6408x^11+2465x^12+500x^13+110x^14+4x^15+4x^16
The gray image is a linear code over GF(2) with n=36, k=16 and d=8.
This code was found by Heurico 1.13 in 0.172 seconds.