The generator matrix

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

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+126x^45+334x^46+778x^47+1105x^48+1460x^49+2066x^50+2530x^51+2863x^52+3322x^53+3531x^54+3316x^55+3145x^56+2530x^57+1986x^58+1488x^59+982x^60+584x^61+270x^62+202x^63+91x^64+42x^65+4x^66+6x^67+3x^68+1x^70+1x^72+1x^80

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 32.2 seconds.