The generator matrix

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

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+29x^10+67x^12+64x^13+711x^14+64x^15+54x^16+27x^18+5x^20+1x^22+1x^24

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.