The generator matrix

 1  0  0  1  1  1 X^2+X  X  1  1  1  X  1  0 X^2  1  1  1 X^2+X  1 X^2+X X^2 X^2+X  1  1  1  0  1 X^2+X X^2+X  1  0  1  1  1  1  0 X^2+X  1 X^2  X X^2  1  1  1 X^2+X  1  1  1  1 X^2  1  1  0  0  1 X^2+X  1  1 X^2 X^2+X
 0  1  0  0  1 X+1  1  0 X^2+1 X+1 X^2+X  1 X^2+X  1  X X+1 X^2  1  1 X^2+X  1  1  0 X+1 X^2+X  1  1  1 X^2+X  1 X^2  X X^2 X^2+X+1  X X^2+1  1  1 X^2+X+1  1  1  1 X+1  0  1  1 X^2+X  1 X^2+X  1  0 X^2+X+1 X^2+X X^2  1  1 X^2+X X^2+1  X  1  1
 0  0  1  1  1 X^2  1  1 X^2+X+1 X^2+X  X X^2+X  1 X^2+1  1 X^2+1  1 X^2  1 X^2+X X^2 X^2+X  1  X X^2+X+1 X^2+X+1 X+1  0  1 X^2+X+1  0  1  0 X^2 X+1 X^2+1  1 X^2+X  1 X^2+X  X  0 X+1 X^2+X  X X^2+X+1 X^2+1  X X+1 X^2+X  1 X^2 X^2+1  1  X X^2+X  1  0 X^2+X X+1 X^2+X
 0  0  0  X X^2+X  0  X X^2+X X^2+X  0  0  0  X  X  X X^2 X^2  X  0 X^2+X X^2+X X^2+X  0  X X^2  0  0 X^2 X^2  X  X X^2+X  X X^2+X  X X^2  X X^2+X X^2+X  X X^2  0 X^2+X X^2  X X^2 X^2+X X^2+X X^2  0  0  0  0 X^2+X X^2  X  X X^2+X X^2+X X^2+X  X
 0  0  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 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0  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+184x^55+200x^56+384x^57+437x^58+460x^59+370x^60+434x^61+272x^62+324x^63+234x^64+274x^65+152x^66+124x^67+84x^68+88x^69+33x^70+12x^71+5x^72+18x^73+1x^74+2x^77+1x^78+2x^80

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 0.76 seconds.