The generator matrix

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

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+46x^11+86x^12+274x^13+63x^14+18x^15+9x^16+14x^17+1x^22

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 0 seconds.