The generator matrix
1 1 1 1 1 1 1 1 X 1
0 X 0 0 0 0 0 X^2+X X^2 0
0 0 X 0 0 0 0 X X X^2
0 0 0 X 0 0 0 X X^2+X X^2
0 0 0 0 X 0 X 0 X^2 0
0 0 0 0 0 X X 0 X X^2
0 0 0 0 0 0 X^2 X^2 0 X^2
generates a code of length 10 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+55x^4+146x^5+261x^6+580x^7+993x^8+3390x^9+5581x^10+3320x^11+965x^12+622x^13+295x^14+132x^15+34x^16+2x^17+7x^18
The gray image is a linear code over GF(2) with n=40, k=14 and d=8.
This code was found by Heurico 1.16 in 0.258 seconds.