The generator matrix

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

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+127x^4+456x^5+1618x^6+3680x^7+4671x^8+3568x^9+1676x^10+480x^11+97x^12+8x^13+2x^14

The gray image is a linear code over GF(2) with n=32, k=14 and d=8.
As d=9 is an upper bound for linear (32,14,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 14.
This code was found by Heurico 1.13 in 0.031 seconds.