The generator matrix

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

generates a code of length 54 over Z2[X]/(X^3) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+28x^53+78x^54+14x^56+4x^61+2x^62+1x^64

The gray image is a linear code over GF(2) with n=216, k=7 and d=106.
This code was found by Heurico 1.16 in 33.5 seconds.