The generator matrix

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

generates a code of length 7 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+21x^4+32x^6+128x^7+67x^8+7x^12

The gray image is a linear code over GF(2) with n=28, k=8 and d=8.
This code was found by Heurico 1.16 in 0.000213 seconds.