The generator matrix

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

generates a code of length 36 over Z2[X]/(X^3) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+135x^28+428x^30+32x^31+662x^32+288x^33+1100x^34+704x^35+1488x^36+704x^37+1160x^38+288x^39+677x^40+32x^41+284x^42+161x^44+36x^46+11x^48+1x^56

The gray image is a linear code over GF(2) with n=144, k=13 and d=56.
This code was found by Heurico 1.16 in 2.33 seconds.