The generator matrix

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

generates a code of length 13 over Z2[X]/(X^4) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+36x^12+64x^13+16x^14+11x^16

The gray image is a linear code over GF(2) with n=104, k=7 and d=48.
As d=51 is an upper bound for linear (104,7,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 7.
This code was found by Heurico 1.16 in 3.81e-009 seconds.