The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1 X^2+X  X  X
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X X^3+1  1  0  0
 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  0 X^3  0 X^3  0 X^3
 0  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0
 0  0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3 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+46x^10+64x^11+326x^12+1216x^13+806x^14+1216x^15+303x^16+64x^17+42x^18+10x^20+2x^22

The gray image is a linear code over GF(2) with n=112, k=12 and d=40.
This code was found by Heurico 1.16 in 0.031 seconds.