The generator matrix

 1  1  1  1  X  1  1 X^2  X  X  1  1  1  1
 0 X^3+X^2  0 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2  0  0
 0  0 X^3  0  0  0  0  0 X^3 X^3 X^3  0  0  0
 0  0  0 X^3  0  0  0  0 X^3 X^3  0 X^3  0  0
 0  0  0  0 X^3  0  0 X^3 X^3 X^3  0  0  0  0
 0  0  0  0  0 X^3  0 X^3 X^3  0 X^3  0  0  0
 0  0  0  0  0  0 X^3 X^3  0 X^3  0 X^3  0  0

generates a code of length 14 over Z2[X]/(X^4) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+26x^8+64x^10+32x^11+101x^12+480x^13+640x^14+480x^15+101x^16+32x^17+64x^18+26x^20+1x^28

The gray image is a linear code over GF(2) with n=112, k=11 and d=32.
This code was found by Heurico 1.16 in 3.81e-009 seconds.