The generator matrix

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

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+28x^11+190x^12+72x^13+190x^14+28x^15+1x^16+2x^18

The gray image is a linear code over GF(2) with n=104, k=9 and d=44.
This code was found by Heurico 1.16 in 3.62e-008 seconds.