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

generates a code of length 61 over Z2[X]/(X^3) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+135x^56+456x^60+256x^62+87x^64+88x^68+1x^120

The gray image is a linear code over GF(2) with n=244, k=10 and d=112.
This code was found by Heurico 1.16 in 10.2 seconds.