The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X 1 1 X 1 1 X X 1 1 X X X^2 X 1 X X X^2 1 X X X^3 X^2 0 X^2 X X^2 X X^3 X^2 X^2 X^3 0 1
0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 0 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 0 0 0 X^3 X^3 X^3 0
generates a code of length 55 over Z2[X]/(X^4) who´s minimum homogenous weight is 56.
Homogenous weight enumerator: w(x)=1x^0+16x^56+10x^57+2x^58+2x^59+1x^60
The gray image is a linear code over GF(2) with n=440, k=5 and d=224.
This code was found by Heurico 1.16 in 0.063 seconds.