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.