The generator matrix

 1  0  0  0  1  1  1 X^2  1  1  1  1  X  X X^2+X  X X^2  1  1  1  1  X  X  1  1  X  X  1  1  1 X^2+X X^2  0  X X^2+X  1  1  1  1 X^2  1  1  X X^2+X  0  1  1  1  1  1 X^2 X^2+X X^2  1  1  1  1  1  1  X  1
 0  1  0  0  1  X  1  1 X^2 X^2+1  0 X+1  1 X^2+X  1  1  1 X+1  X  1  0  1 X^2+X X^2+X+1 X^2+1  1  X  0 X+1 X^2  1  0 X^2  1  1 X+1 X+1  X  1  1 X^2+X  X  0 X^2+X X^2+X  1 X+1  X  X X^2+X  1 X^2+X  X  1 X^2+1 X+1 X^2 X+1 X^2+1  1  0
 0  0  1  0  X  1 X+1  1 X^2+1 X^2 X^2+X X+1  X  1  1  0 X+1 X^2+1 X^2  X X^2 X^2+X X^2  1 X^2 X^2+X+1  1  1  0 X^2+X+1 X^2+1  1  1  1 X^2+X X^2+X+1  X X^2+X+1 X^2+X+1 X^2+X  X  1  0  X  0  1 X^2+X  X X^2+1 X^2+X X^2+X  1  1 X^2+X+1 X^2+X+1 X^2+X X^2+X  X  1 X^2+X+1  X
 0  0  0  1  X X^2+X X^2  1  1 X+1 X+1 X^2+1 X+1 X^2+X+1 X^2+X X^2+1 X^2+1  0  1  0 X^2+X  0  1 X^2+X+1 X^2  X  1 X^2+X+1 X+1  0  1  1 X^2+X X^2+X X+1 X^2+X  1 X^2 X^2+1 X^2+X  1 X^2+1  1  1  1 X^2  0 X^2+X X+1 X^2  1 X^2+X  0 X+1  X X^2+X  0 X^2+X+1  1 X^2+X+1  1
 0  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 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 54.

Homogenous weight enumerator: w(x)=1x^0+157x^54+310x^55+621x^56+578x^57+784x^58+696x^59+800x^60+618x^61+876x^62+562x^63+620x^64+426x^65+442x^66+238x^67+181x^68+134x^69+105x^70+16x^71+14x^72+4x^73+2x^74+2x^75+3x^76+2x^78

The gray image is a linear code over GF(2) with n=244, k=13 and d=108.
This code was found by Heurico 1.11 in 0.984 seconds.