The generator matrix
1 0 1 1 1 0 X X
0 1 1 0 X+1 1 X^2 X^2
0 0 X 0 X 0 0 X^2
0 0 0 X X X^2+X X X^2+X
0 0 0 0 X^2 0 X^2 0
0 0 0 0 0 X^2 X^2 0
generates a code of length 8 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+83x^4+128x^5+422x^6+896x^7+1031x^8+896x^9+436x^10+128x^11+69x^12+6x^14
The gray image is a linear code over GF(2) with n=32, k=12 and d=8.
This code was found by Heurico 1.16 in 0.00944 seconds.