The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1
 0 X^3  0  0  0 X^3  0  0 X^3 X^3  0  0 X^3
 0  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3
 0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0
 0  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0

generates a code of length 13 over Z2[X]/(X^4) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+7x^10+8x^12+224x^13+8x^14+7x^16+1x^26

The gray image is a linear code over GF(2) with n=104, k=8 and d=40.
This code was found by Heurico 1.16 in 3.81e-009 seconds.