The generator matrix
1 0 1 1 1 X^2 1 1 X^2 1
0 1 1 0 X+1 1 0 X+1 1 0
0 0 X 0 X X^2 X X^2 X 0
0 0 0 X X X^2+X X^2+X X^2 0 0
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+26x^6+46x^7+105x^8+212x^9+244x^10+208x^11+110x^12+44x^13+26x^14+2x^15
The gray image is a linear code over GF(2) with n=40, k=10 and d=12.
This code was found by Heurico 1.16 in 0.0029 seconds.