The generator matrix

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

generates a code of length 36 over Z2[X]/(X^3) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+111x^26+331x^28+678x^30+128x^31+1316x^32+640x^33+2309x^34+1280x^35+2731x^36+1280x^37+2356x^38+640x^39+1459x^40+128x^41+585x^42+265x^44+102x^46+39x^48+3x^50+1x^52+1x^56

The gray image is a linear code over GF(2) with n=144, k=14 and d=52.
This code was found by Heurico 1.16 in 23.4 seconds.