The generator matrix
1 0 0 1 1 1 1 X 1 1 1
0 1 0 1 0 1 0 1 X+1 0 X^2
0 0 1 1 1 0 0 1 0 X 0
0 0 0 X 0 0 X^2 X X X^2+X 0
0 0 0 0 X 0 X^2+X X X^2+X X^2+X 0
0 0 0 0 0 X X X^2 0 X^2+X X^2+X
generates a code of length 11 over Z2[X]/(X^3) who´s minimum homogenous weight is 5.
Homogenous weight enumerator: w(x)=1x^0+38x^5+125x^6+480x^7+1265x^8+3606x^9+6825x^10+8176x^11+6747x^12+3506x^13+1303x^14+560x^15+114x^16+18x^17+3x^18+1x^20
The gray image is a linear code over GF(2) with n=44, k=15 and d=10.
This code was found by Heurico 1.16 in 0.885 seconds.