The generator matrix
1 1 1 1 1 1 1
0 X 0 0 0 X 0
0 0 X 0 0 X 0
0 0 0 X 0 X 0
0 0 0 0 X X 0
0 0 0 0 0 X^2 0
generates a code of length 7 over Z2[X]/(X^3) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+45x^2+20x^3+211x^4+240x^5+255x^6+2552x^7+255x^8+240x^9+211x^10+20x^11+45x^12+1x^14
The gray image is a linear code over GF(2) with n=28, k=12 and d=4.
This code was found by Heurico 1.16 in 0.00622 seconds.