The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1  1  1  1  1  1  1  1  1  1 X^2  1  1  0  1 X^2
 0  X  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  X X^2+X X^2+X  X  X  X X^2+X X^2+X X^2+X  X  X  0  X  X X^2 X^2+X  0
 0  0  X  0  0  0  0  0  0  0  X X^2+X  X X^2+X X^2+X  X X^2+X  0  X X^2+X  X X^2+X X^2 X^2  0 X^2  0  X X^2  0 X^2  X  X  X X^2+X  X
 0  0  0  X  0  0  0  X X^2+X  X  X  X  0 X^2+X  X  0  0  X X^2  X  X X^2+X X^2+X X^2+X X^2+X X^2+X  0  X X^2 X^2 X^2 X^2 X^2 X^2  X X^2+X
 0  0  0  0  X  0  X  X  X X^2  0  0 X^2 X^2+X  X X^2+X  X  X X^2 X^2 X^2+X  X X^2+X  0  X  0  0 X^2+X  X  0  X X^2  0 X^2 X^2  X
 0  0  0  0  0  X  X X^2 X^2+X X^2+X  0  X  X  X X^2  0  X  X  X X^2  X X^2  X  0  0 X^2+X  X X^2+X  0  0 X^2+X  0 X^2 X^2  0 X^2+X
 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  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0  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 27.

Homogenous weight enumerator: w(x)=1x^0+86x^27+202x^28+288x^29+327x^30+424x^31+701x^32+866x^33+1442x^34+2336x^35+2772x^36+2456x^37+1596x^38+1060x^39+664x^40+396x^41+300x^42+170x^43+130x^44+88x^45+44x^46+20x^47+10x^48+2x^49+2x^50+1x^62

The gray image is a linear code over GF(2) with n=144, k=14 and d=54.
This code was found by Heurico 1.16 in 46.3 seconds.