The generator matrix

 1  0  1  1  1 X^3 X^2+X  1  1 X^3+X^2+X  X  1  1
 0  1 X+1 X^3+X^2+X X^2+1  1  1 X^3 X^2+X  1  X X^2 X^3+X^2
 0  0 X^2 X^3+X^2 X^3 X^2  0 X^2  0 X^3+X^2 X^3+X^2 X^3+X^2 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+124x^11+201x^12+404x^13+168x^14+100x^15+13x^16+12x^17+1x^20

The gray image is a linear code over GF(2) with n=104, k=10 and d=44.
This code was found by Heurico 1.16 in 0.047 seconds.