The generator matrix

 1  0  0  0  0  1  1  1  0  1 X^2  1  1 X^2  0  1  1 X^2+X X^2 X^2  1  X  X  X  1  1 X^2  1  X  1 X^2+X  1 X^2 X^2+X  1  1 X^2+X X^2 X^2  X  1  1  1  1  1 X^2+X  1  1  1 X^2  1  X  1  1
 0  1  0  0  0  0  0 X^2 X^2  1  1  1  1  1  1 X+1 X^2+X+1 X^2+X  1  1  0 X^2+X  1  X X+1  0 X^2+X X^2+1  1 X^2+X  1 X^2 X^2  1  X  0 X^2+X  0  X X^2 X^2+1 X+1  X X^2+X X+1 X^2  1  X X^2+1 X^2+X X^2+X+1  1  X  0
 0  0  1  0  0 X^2  1 X^2+1  1  0  1 X+1 X^2+X+1 X^2 X^2+X+1  X  X  1 X^2+X+1 X^2  X  1  1 X^2+X  X X+1  X  1 X^2 X^2+X  0  1 X^2+X  0  0  1  1  1  X  1  X X^2+X+1  X X+1 X^2  1  1 X^2 X^2+1  1  0  0  0  0
 0  0  0  1  0 X^2+1  1  0  1 X^2 X^2+1 X+1 X^2+X X^2+X+1 X^2 X^2+X+1 X^2+1  1 X^2+1  X X^2 X^2 X^2+X  1  0 X+1  1  0 X^2+1  1 X^2+X X+1  1 X^2+1 X^2+X  X X+1 X^2+1 X^2  X  1  X X+1  0 X^2+X+1  1  0 X^2 X+1  X  0 X+1 X^2+X+1  0
 0  0  0  0  1  1 X^2  1  1 X^2+1 X^2  1 X^2+X  1 X+1  0 X^2+1  0  1 X^2+X+1 X^2+X+1  1 X^2+X  1 X^2+X X^2+X+1 X^2+X X+1 X^2  0 X^2  1  1  X  0 X^2+X X^2+X+1 X^2+X+1  1 X^2  X X^2+1 X^2+1 X+1 X^2+X  X  X X^2+X  0  X  X X^2 X^2+1 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+52x^45+331x^46+656x^47+1226x^48+1680x^49+2186x^50+2438x^51+2958x^52+3066x^53+3473x^54+3266x^55+3075x^56+2532x^57+2204x^58+1376x^59+1020x^60+630x^61+314x^62+140x^63+96x^64+24x^65+4x^66+10x^67+8x^68+2x^71

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 31.6 seconds.