The generator matrix

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

generates a code of length 9 over Z2[X]/(X^4) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+36x^4+254x^8+1536x^9+128x^10+84x^12+9x^16

The gray image is a linear code over GF(2) with n=72, k=11 and d=16.
This code was found by Heurico 1.16 in 0.016 seconds.