The generator matrix

 1  1  1  1  1  1  X  0  1  1  X  0  X  X
 0  X X^3+X^2 X^2+X  0 X^2+X X^2+X  X X^3+X^2 X^3+X X^3+X  X  0 X^3+X^2
 0  0 X^3  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0
 0  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0
 0  0  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0
 0  0  0  0  0 X^3 X^3  0 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+30x^10+64x^11+198x^12+448x^13+582x^14+448x^15+175x^16+64x^17+26x^18+10x^20+2x^22

The gray image is a linear code over GF(2) with n=112, k=11 and d=40.
This code was found by Heurico 1.16 in 0.016 seconds.