The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  1  1 X^3  1  1  1 X^2+X
 0  1 X+1 X^2+X X^2+1  1 X^2+X+1 X^3+1 X^3  1 X^3+X^2+1 X^3+X^2+X  1  1
 0  0 X^2  0 X^3 X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^2 X^2 X^3+X^2  0
 0  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3  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+294x^12+384x^13+704x^14+384x^15+271x^16+10x^20

The gray image is a linear code over GF(2) with n=112, k=11 and d=48.
As d=51 is an upper bound for linear (112,11,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 11.
This code was found by Heurico 1.16 in 0.016 seconds.