The generator matrix

 1  0  0  0  1  1  1  0
 0  1  0  0  X  1  1  1
 0  0  1  0 X+1  1  X  1
 0  0  0  1  1 X^2+X X+1  1
 0  0  0  0 X^2  0  0 X^2
 0  0  0  0  0 X^2  0 X^2
 0  0  0  0  0  0 X^2 X^2

generates a code of length 8 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+204x^4+1280x^5+2240x^6+8960x^7+7398x^8+8960x^9+2240x^10+1280x^11+204x^12+1x^16

The gray image is a linear code over GF(2) with n=32, k=15 and d=8.
As d=8 is an upper bound for linear (32,15,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 15.
This code was found by Heurico 1.16 in 0.478 seconds.