The generator matrix

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

generates a code of length 13 over Z2[X]/(X^3) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+44x^11+71x^12+52x^13+45x^14+22x^15+8x^16+8x^17+3x^18+2x^19

The gray image is a linear code over GF(2) with n=52, k=8 and d=22.
This code was found by Heurico 1.16 in 0.0015 seconds.