The generator matrix
1 1 1 1 1 X 1 1 1
0 X 0 0 0 X^2 X X^2 0
0 0 X 0 0 X X X^2+X 0
0 0 0 X 0 X 0 X^2 0
0 0 0 0 X X X^2 X 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+22x^4+62x^5+67x^6+108x^7+423x^8+676x^9+422x^10+128x^11+64x^12+46x^13+23x^14+4x^15+2x^16
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 0.00424 seconds.