The generator matrix

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

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+56x^26+84x^27+205x^28+316x^29+448x^30+646x^31+993x^32+1192x^33+1460x^34+1776x^35+1822x^36+1872x^37+1607x^38+1364x^39+888x^40+632x^41+456x^42+204x^43+169x^44+84x^45+62x^46+22x^47+14x^48+4x^50+4x^52+3x^54

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 8.46 seconds.