The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  X  X X^2
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0 X^3 X^3 X^2 X^2 X^3+X^2
 0  0 X^3+X^2  0 X^2 X^2 X^2 X^3  0 X^3  0 X^2 X^3+X^2  0
 0  0  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^2  0  0 X^3
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 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+37x^10+82x^11+131x^12+432x^13+698x^14+436x^15+113x^16+64x^17+33x^18+10x^19+11x^20

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.