The generator matrix
1 1 1 1 1 1 X X 1 1
0 X 0 0 0 X X^2 0 X X
0 0 X 0 X X X X^2 X X^2+X
0 0 0 X X 0 0 X X^2 X
0 0 0 0 X^2 0 X^2 0 0 X^2
0 0 0 0 0 X^2 X^2 X^2 0 X^2
generates a code of length 10 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+97x^6+292x^8+256x^9+751x^10+256x^11+308x^12+79x^14+7x^16+1x^18
The gray image is a linear code over GF(2) with n=40, k=11 and d=12.
This code was found by Heurico 1.16 in 0.102 seconds.