The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1
 0 X^3+X^2  0 X^2  0 X^3 X^2 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^3
 0  0 X^3+X^2 X^2 X^3 X^2  0 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3  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+6x^11+15x^12+212x^13+15x^14+6x^15+1x^26

The gray image is a linear code over GF(2) with n=104, k=8 and d=44.
This code was found by Heurico 1.16 in 6.87e-008 seconds.