The generator matrix
1 1 1 1 1 X X X 1 0 X X 1 1
0 X 0 X 0 0 X X^2+X X^2 0 X^2 X^2 0 0
0 0 X X 0 X X 0 X X X X 0 0
0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0
0 0 0 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0
0 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0
0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0
generates a code of length 14 over Z2[X]/(X^3) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+34x^8+144x^10+32x^11+349x^12+224x^13+480x^14+224x^15+349x^16+32x^17+144x^18+34x^20+1x^28
The gray image is a linear code over GF(2) with n=56, k=11 and d=16.
This code was found by Heurico 1.16 in 0.0153 seconds.