The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  X  X  1
 0 X^3+X^2  0 X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3  0 X^2 X^2  0
 0  0 X^3+X^2 X^2  0 X^2 X^2 X^3  0 X^2 X^3+X^2 X^2 X^3+X^2  0
 0  0  0 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3  0
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0

generates a code of length 14 over Z2[X]/(X^4) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+28x^10+38x^11+41x^12+92x^13+625x^14+88x^15+49x^16+36x^17+18x^18+2x^19+5x^20+1x^22

The gray image is a linear code over GF(2) with n=112, k=10 and d=40.
This code was found by Heurico 1.16 in -1.01e-007 seconds.