The generator matrix

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

generates a code of length 14 over Z2[X]/(X^4) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+118x^12+276x^14+112x^16+4x^18+1x^24

The gray image is a linear code over GF(2) with n=112, k=9 and d=48.
This code was found by Heurico 1.16 in 0 seconds.