The generator matrix

 1  0  0  1  1  1  X  1  1 X^2+X  1 X^2  1 X^2
 0  1  0  1  X X^2+X+1  1 X^2+X  0  1  1  1  X  1
 0  0  1  1  1  0  1  X X+1 X+1 X^2+X X+1 X+1  0
 0  0  0  X  0 X^2+X X^2 X^2+X X^2  0 X^2  X X^2+X X^2+X
 0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0

generates a code of length 14 over Z2[X]/(X^3) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+131x^10+208x^11+561x^12+696x^13+910x^14+696x^15+581x^16+168x^17+111x^18+24x^19+9x^20

The gray image is a linear code over GF(2) with n=56, k=12 and d=20.
This code was found by Heurico 1.16 in 0.105 seconds.