The generator matrix

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

generates a code of length 55 over Z2[X]/(X^4) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+340x^53+126x^54+112x^55+124x^56+292x^57+2x^58+24x^59+1x^64+2x^76

The gray image is a linear code over GF(2) with n=440, k=10 and d=212.
This code was found by Heurico 1.16 in 1.59 seconds.