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.