The generator matrix

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

generates a code of length 36 over Z2[X]/(X^3) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+6x^29+50x^30+18x^31+64x^32+38x^33+21x^34+322x^35+21x^36+322x^37+25x^38+38x^39+22x^40+18x^41+10x^42+6x^43+10x^44+20x^46+9x^48+1x^50+1x^52+1x^54

The gray image is a linear code over GF(2) with n=144, k=10 and d=58.
This code was found by Heurico 1.16 in 16.5 seconds.