The generator matrix

 1  1  1  1  1  1  1  1 X^3
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X X^3
 0  0 X^3 X^3 X^3  0  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+142x^8+96x^10+16x^12+1x^16

The gray image is a linear code over GF(2) with n=72, k=8 and d=32.
As d=32 is an upper bound for linear (72,8,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 8.
This code was found by Heurico 1.16 in -6.48e-008 seconds.