The generator matrix

 1  0  0  0  0  1  1  1  0 X^2  1  1  1  0  0  1  1 X^2+X  1  0  1  1  0  X  1  X  1 X^2  1  1  X X^2+X  0  X  1 X^2  1  1 X^2  1 X^2  X X^2+X X^2+X  1  1  1  0  0  1  1  1  1  1
 0  1  0  0  0  0  0  0 X^2  0  0 X^2  0  0 X^2  X  1  1 X+1  1  1 X+1  1  1 X+1  1  1  1 X^2+1  1  X X^2 X^2+X  1 X^2+X  X X^2+X+1 X+1  1  0 X^2  1  X  1  0 X^2+1 X^2+X X^2+X  1 X^2+X+1  X X+1 X^2+X X^2+X
 0  0  1  0  0  0  1  1  1  1 X^2 X^2+X+1 X+1  1  X  X X^2+X  X X^2+X X^2+X+1  0 X^2+X+1  1 X^2 X^2+X+1 X^2+X+1  0  X X+1 X+1  1  X  1 X^2+X+1 X^2+X  0  0 X+1  X X+1  1  0  0 X^2 X^2+X+1 X^2 X^2+X+1  1 X^2+1 X^2  X X^2+1  1 X^2+X
 0  0  0  1  0  1  1 X^2 X^2+1 X^2+1  X  1  X X^2+X  1 X+1 X^2  0 X+1 X^2 X+1  1 X^2+X+1 X^2+X+1  0 X^2+X  0 X+1  X X^2+1 X^2+X  1  1 X+1  1  0 X^2+X  0 X^2+1  0  X X^2+X  0 X^2+X+1 X^2 X^2+1 X^2+X+1 X^2+X+1  X  0  0  1 X^2+X+1 X^2+X+1
 0  0  0  0  1  1 X^2 X^2+1 X^2+1  X X^2+X+1 X^2+X+1  0 X+1 X+1 X^2 X+1 X^2+1 X^2+X  1 X^2+X+1 X^2  1  X X+1 X^2  X X+1  0 X^2+1 X+1  X  1 X^2+X X^2  1 X^2 X+1 X^2+X+1 X^2+X X^2+X+1 X^2+X  1 X^2  1 X^2 X^2+1  0 X^2+X  1 X^2+1  X X^2 X^2+X+1
 0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 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+344x^45+808x^46+1376x^47+2362x^48+2758x^49+4126x^50+4554x^51+6151x^52+6190x^53+7738x^54+6336x^55+6488x^56+4988x^57+4298x^58+2638x^59+1978x^60+1072x^61+658x^62+382x^63+165x^64+70x^65+32x^66+8x^67+7x^68+2x^69+4x^70+2x^71

The gray image is a linear code over GF(2) with n=216, k=16 and d=90.
This code was found by Heurico 1.13 in 611 seconds.