The generator matrix

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

generates a code of length 8 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+9x^6+56x^7+13x^8+32x^9+6x^10+8x^11+2x^12+1x^14

The gray image is a linear code over GF(2) with n=32, k=7 and d=12.
This code was found by Heurico 1.16 in 0.00028 seconds.