The generator matrix

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

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+46x^10+154x^11+202x^12+430x^13+396x^14+416x^15+207x^16+144x^17+38x^18+6x^19+6x^20+2x^21

The gray image is a linear code over GF(2) with n=56, k=11 and d=20.
This code was found by Heurico 1.16 in 0.0187 seconds.