The generator matrix

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

generates a code of length 61 over Z2[X]/(X^3) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+120x^55+290x^56+370x^57+482x^58+360x^59+455x^60+372x^61+328x^62+290x^63+261x^64+186x^65+194x^66+132x^67+103x^68+60x^69+40x^70+26x^71+18x^72+4x^74+4x^77

The gray image is a linear code over GF(2) with n=244, k=12 and d=110.
This code was found by Heurico 1.11 in 0.266 seconds.