The generator matrix
1 1 1 1 1 1 1 1 1 1
0 X^2 0 0 0 0 0 0 0 0
0 0 X^2 0 0 0 0 0 0 0
0 0 0 X^2 0 0 0 0 0 0
0 0 0 0 X^2 0 0 0 0 0
0 0 0 0 0 X^2 0 0 0 0
0 0 0 0 0 0 X^2 0 0 0
0 0 0 0 0 0 0 X^2 0 0
0 0 0 0 0 0 0 0 X^2 0
0 0 0 0 0 0 0 0 0 X^2
generates a code of length 10 over Z2[X]/(X^3) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+10x^2+45x^4+120x^6+210x^8+3324x^10+210x^12+120x^14+45x^16+10x^18+1x^20
The gray image is a linear code over GF(2) with n=40, k=12 and d=4.
This code was found by Heurico 1.16 in 0.0101 seconds.