The generator matrix

 1  1  1  1  1  X  0  1  1  1  1  1  X  1
 0  X X^3+X^2 X^2+X  0 X^2+X  X X^3+X^2  0  0 X^3 X^2+X X^2+X  0
 0  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0
 0  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0
 0  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3  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+21x^10+8x^11+114x^12+152x^13+436x^14+152x^15+108x^16+8x^17+21x^18+2x^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 -3.24e-008 seconds.