The generator matrix

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

generates a code of length 13 over Z2[X]/(X^4) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+318x^11+276x^12+916x^13+208x^14+288x^15+27x^16+12x^17+2x^19

The gray image is a linear code over GF(2) with n=104, k=11 and d=44.
As d=47 is an upper bound for linear (104,11,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 11.
This code was found by Heurico 1.16 in 3.52 seconds.