The generator matrix

 1  0  0  0  0  1  1  1  0  1 X^2  1  1  1  1  0  X  0 X^2+X X^2+X  1 X^2+X  1  1  1 X^2+X X^2  0  X  1  1 X^2 X^2  0  1  1
 0  1  0  0  0  0 X+1  X X^2 X+1  1 X^2 X^2+1 X+1 X^2+X+1  1  1  1 X^2  1 X^2+X+1  1  1  0 X^2+1  X X^2+X  1  X X^2+X  X  1  0  1 X^2+1  0
 0  0  1  0  0  0  1 X+1  1 X^2+1 X^2 X^2+1 X^2+X X^2+X+1 X^2+X  X X^2+1 X+1  1 X^2+X  0 X^2+1 X+1  X  0 X^2+X  1 X^2+X+1 X^2+X X^2 X^2+X+1  0  1 X^2+1 X^2+X+1  0
 0  0  0  1  0  1 X^2 X^2+1  1 X+1 X^2+1 X^2+X X^2 X^2+1 X^2+X+1 X^2+X  0 X^2+1 X^2+1 X^2+X+1 X^2+X+1 X+1  0 X+1  0  1 X^2+1  0  1  X X^2+X+1 X+1 X^2+X  0  1 X^2
 0  0  0  0  1  1 X^2+1  X X+1 X^2+1 X^2+X X^2+1  0 X^2 X^2+X+1 X^2+1 X^2 X+1 X^2  1 X^2+X X^2+X  0 X^2 X^2+X+1 X^2+1  X  1  0  1  1  X X^2+1  X X^2+X  0
 0  0  0  0  0  X  0  X  X X^2+X  X X^2  0  X X^2+X  0 X^2 X^2+X X^2+X X^2  0  0 X^2+X X^2 X^2+X X^2 X^2 X^2+X X^2+X  X X^2  0  0 X^2  0 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+118x^27+559x^28+1284x^29+2610x^30+4424x^31+7263x^32+10402x^33+13358x^34+16262x^35+17514x^36+16682x^37+14132x^38+10906x^39+7152x^40+4214x^41+2345x^42+1036x^43+527x^44+186x^45+66x^46+22x^47+8x^48+1x^58

The gray image is a linear code over GF(2) with n=144, k=17 and d=54.
This code was found by Heurico 1.13 in 91.6 seconds.