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 X 0 X 0 X 0 X 0 X X^2 X 0 X 0 X^2 X X^2 1 1 1 1 X 1
0 X 0 X^2+X 0 X^2+X 0 X 0 X^2+X 0 X 0 X^2+X 0 X X^2 X^2+X X^2 X X^2 X^2+X X^2 X X^2 X^2+X X^2 X X^2 X^2+X X^2 X X^2+X X X^2+X X X^2+X X X^2+X X X X X^2+X X X^2+X X 0 X X 0 0 0 X^2 X^2 0
0 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 0
0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0
0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 0 0 0
generates a code of length 55 over Z2[X]/(X^3) who´s minimum homogenous weight is 52.
Homogenous weight enumerator: w(x)=1x^0+52x^52+16x^53+74x^54+32x^55+10x^56+16x^57+18x^58+32x^60+2x^62+1x^64+2x^74
The gray image is a linear code over GF(2) with n=220, k=8 and d=104.
This code was found by Heurico 1.16 in 0.0848 seconds.