The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  X  X  X
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  X  X X^2
 0  0  X  0  X  X  X X^2  0 X^2  0  X X^2+X X^2+X
 0  0  0  X  X X^2 X^2+X X^2+X  0 X^2+X  X  0 X^2 X^2+X
 0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 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+37x^10+82x^11+131x^12+176x^13+186x^14+180x^15+113x^16+64x^17+33x^18+10x^19+11x^20

The gray image is a linear code over GF(2) with n=56, k=10 and d=20.
This code was found by Heurico 1.16 in 0.00883 seconds.