The generator matrix

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

generates a code of length 54 over Z2[X]/(X^3) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+19x^48+60x^49+63x^50+52x^51+111x^52+172x^53+153x^54+110x^55+97x^56+70x^57+27x^58+24x^59+21x^60+16x^61+11x^62+6x^63+7x^64+2x^65+1x^66+1x^98

The gray image is a linear code over GF(2) with n=216, k=10 and d=96.
This code was found by Heurico 1.16 in 0.136 seconds.