The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  1  1
 0 X^3+X^2  0 X^3+X^2  0 X^3 X^3+X^2 X^2  0 X^3+X^2 X^3+X^2 X^3  0  0
 0  0 X^3  0  0 X^3  0  0  0 X^3 X^3  0 X^3  0
 0  0  0 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0
 0  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3  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+9x^10+8x^11+18x^12+56x^13+332x^14+56x^15+11x^16+8x^17+10x^18+2x^20+1x^26

The gray image is a linear code over GF(2) with n=112, k=9 and d=40.
This code was found by Heurico 1.16 in -1.01e-007 seconds.