The generator matrix

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

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+96x^55+308x^56+384x^57+478x^58+316x^59+532x^60+358x^61+324x^62+256x^63+295x^64+168x^65+194x^66+120x^67+108x^68+64x^69+40x^70+26x^71+20x^72+4x^74+2x^77+2x^79

The gray image is a linear code over GF(2) with n=244, k=12 and d=110.
This code was found by Heurico 1.16 in 0.616 seconds.