The generator matrix

 1  1  1  1  1  1  X X^3  1  1  X  X  X  X
 0  X  0 X^2+X X^2 X^3+X^2 X^3+X^2+X  X X^3+X^2+X X^3+X^2+X X^2+X X^3+X  0  0
 0  0 X^3+X^2  0 X^2 X^3 X^2 X^3+X^2 X^3+X^2 X^3+X^2  0 X^3  0  0
 0  0  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0  0
 0  0  0  0 X^3  0  0 X^3  0 X^3 X^3 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+50x^10+32x^11+194x^12+480x^13+542x^14+480x^15+183x^16+32x^17+46x^18+6x^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 0.015 seconds.