The generator matrix

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

generates a code of length 54 over Z2[X]/(X^3) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+116x^45+335x^46+756x^47+1073x^48+1668x^49+1944x^50+2624x^51+2624x^52+3562x^53+3218x^54+3514x^55+2955x^56+2766x^57+2000x^58+1558x^59+843x^60+618x^61+257x^62+178x^63+83x^64+30x^65+20x^66+10x^67+5x^68+8x^69+2x^70

The gray image is a linear code over GF(2) with n=216, k=15 and d=90.
This code was found by Heurico 1.16 in 33.3 seconds.