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  1  1  1  X X^2  1  1  1  1  1  1  X  1  X  1
 0  X  0  X  0  0  X X^2+X X^2 X^2  X X^2+X X^2+X X^2+X X^2 X^2  0  X X^2  X  X X^2  0  X X^2+X  X  0  0  0  X  0 X^2+X  0 X^2 X^2  0  0 X^2 X^2  0  X  X  X  X X^2+X X^2+X X^2 X^2  0  0  X  0  X  0
 0  0  X  X  0 X^2+X  X X^2  0  X  X  0 X^2  X X^2 X^2+X  0 X^2+X X^2+X X^2 X^2 X^2+X  0 X^2+X  0  0  0 X^2  X  X  X  X  0  X X^2 X^2+X X^2 X^2+X  0  X  X  X X^2+X X^2+X X^2+X X^2+X  X  X X^2+X X^2+X  X X^2 X^2+X  0
 0  0  0 X^2  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0
 0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2  0  0  0  0 X^2 X^2  0 X^2
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  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+50x^48+124x^50+32x^51+84x^52+224x^53+16x^54+224x^55+72x^56+32x^57+112x^58+40x^60+5x^64+4x^66+3x^68+1x^100

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 0.138 seconds.