The generator matrix

 1  0  1  1  1  1  1  1  1  1
 0  1 X+1  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+22x^2+141x^4+456x^6+882x^8+3072x^9+7236x^10+3072x^11+882x^12+456x^14+141x^16+22x^18+1x^20

The gray image is a linear code over GF(2) with n=40, k=14 and d=4.
This code was found by Heurico 1.16 in 0.0809 seconds.