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 X X^2 1 1 1 1 X 1 1 1 X^2 1 1 1 X X 1 1 0 1 1 1 X 1 0 1 1 X X 1 X X 1
0 X 0 0 0 0 0 X^2 X^2 X X^2+X X X X X^2+X X 0 X^2+X X^2 X X^2 X 0 X X^2 X^2+X X^2+X X^2 X^2+X X^2 X 0 X X^2 X^2+X X X 0 X^2 X^2 0 X^2+X X X^2+X 0 0 0 X 0 X^2 0 X^2 X^2+X 0 X 0 X^2+X X^2 0
0 0 X 0 0 X^2 X^2+X X X X X X X^2+X 0 0 0 X^2 X^2 X^2+X X X^2 0 0 X^2+X X^2 X^2 0 0 0 X^2+X X X^2+X 0 X X^2+X X^2 X^2+X X^2 X X X X X X^2+X X X X^2 X 0 X^2 X 0 X^2+X X^2 X^2 X^2 X^2 X^2 X^2+X
0 0 0 X 0 X^2+X X^2+X X X^2 X^2+X X^2+X 0 0 X X X^2 X X^2 X^2+X 0 X^2+X 0 X^2 X X^2 X 0 X X X X X^2 X X^2 0 X^2+X X^2 0 X^2+X X X^2+X X^2 X 0 X^2 X^2 0 X^2+X X^2 X^2 0 0 0 X X X 0 X X
0 0 0 0 X X X^2 X^2+X X X^2+X X^2 X^2 X X^2 X^2+X X X X^2 X^2 X^2+X 0 X^2+X 0 X^2+X X^2+X X^2+X X^2 X 0 X X^2 X X^2 X^2 0 0 0 X^2 0 X^2 X X X^2+X X^2+X 0 X^2+X 0 0 X^2+X X^2 X^2 0 X X^2 X X^2+X 0 0 X
generates a code of length 59 over Z2[X]/(X^3) who´s minimum homogenous weight is 52.
Homogenous weight enumerator: w(x)=1x^0+41x^52+104x^53+100x^54+154x^55+158x^56+192x^57+246x^58+212x^59+217x^60+148x^61+125x^62+96x^63+64x^64+56x^65+32x^66+30x^67+25x^68+20x^69+9x^70+2x^71+3x^72+8x^73+2x^75+2x^76+1x^92
The gray image is a linear code over GF(2) with n=236, k=11 and d=104.
This code was found by Heurico 1.16 in 0.336 seconds.