The generator matrix

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

generates a code of length 9 over Z2[X]/(X^4) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+18x^8+96x^9+8x^10+4x^12+1x^16

The gray image is a linear code over GF(2) with n=72, k=7 and d=32.
As d=34 is an upper bound for linear (72,7,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 7.
This code was found by Heurico 1.16 in 3.81e-009 seconds.