The generator matrix

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

generates a code of length 14 over Z2[X]/(X^4) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+88x^13+76x^14+88x^15+1x^16+2x^20

The gray image is a linear code over GF(2) with n=112, k=8 and d=52.
As d=54 is an upper bound for linear (112,8,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 8.
This code was found by Heurico 1.16 in -1.01e-007 seconds.