The generator matrix
1 0 0 0 1 1 1 1 X^2+X 1 0
0 1 0 0 1 X X^2+X X+1 1 X^2+X 1
0 0 1 0 1 0 X+1 0 X+1 X+1 1
0 0 0 1 1 1 X X X+1 X+1 X+1
0 0 0 0 X 0 X X^2+X X^2 0 X
0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2
generates a code of length 11 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+103x^6+502x^7+1452x^8+3542x^9+7129x^10+7276x^11+7172x^12+3548x^13+1465x^14+478x^15+79x^16+14x^17+7x^18
The gray image is a linear code over GF(2) with n=44, k=15 and d=12.
This code was found by Heurico 1.16 in 1.2 seconds.