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

generates a code of length 61 over Z2[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+121x^54+24x^55+126x^56+68x^57+201x^58+224x^59+104x^60+380x^61+125x^62+248x^63+91x^64+60x^65+108x^66+16x^67+47x^68+4x^69+81x^70+14x^72+3x^74+1x^78+1x^100

The gray image is a linear code over GF(2) with n=244, k=11 and d=108.
This code was found by Heurico 1.16 in 0.442 seconds.