The generator matrix

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

generates a code of length 13 over Z2[X]/(X^4) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+16x^8+8x^10+46x^12+384x^13+24x^14+23x^16+10x^20

The gray image is a linear code over GF(2) with n=104, k=9 and d=32.
This code was found by Heurico 1.16 in -6.48e-008 seconds.