The generator matrix

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

generates a code of length 13 over Z2[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+55x^8+224x^12+512x^13+128x^14+87x^16+16x^20+1x^24

The gray image is a linear code over GF(2) with n=52, k=10 and d=16.
This code was found by Heurico 1.16 in 0.00383 seconds.