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  1  1  1  1  1  1  1  1  1  1  X  1
 0  X  0 X^2+X X^2 X^3+X^2+X X^3+X^2  X  0 X^2+X X^3+X^2 X^3+X  0  X X^3+X^2 X^3+X^2+X X^3+X^2  X  0 X^3+X^2+X X^3 X^3+X^2+X X^2 X^3+X X^2 X^3+X  0 X^3+X^2+X X^3 X^3+X^2+X X^2 X^3+X X^3+X^2 X^3+X  0 X^2+X X^3 X^2+X X^3+X^2+X X^3 X^2+X  0 X^3+X^2 X^3 X^3 X^2+X X^3+X  X X^3+X X^2+X X^3+X^2 X^2 X^2+X X^3
 0  0 X^3+X^2  0 X^3+X^2 X^2  0 X^2 X^3 X^3 X^3 X^3 X^2 X^3+X^2 X^2 X^3+X^2  0 X^2  0 X^2 X^2 X^3 X^2 X^3 X^3 X^3+X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3  0  0 X^3 X^3+X^2 X^2 X^2  0  0 X^3+X^2  0 X^3 X^2 X^2 X^3 X^3  0 X^2
 0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0  0

generates a code of length 54 over Z2[X]/(X^4) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+18x^51+94x^52+144x^53+516x^54+140x^55+89x^56+16x^57+3x^58+2x^59+1x^106

The gray image is a linear code over GF(2) with n=432, k=10 and d=204.
This code was found by Heurico 1.16 in 0.188 seconds.