The generator matrix

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

generates a code of length 61 over Z2[X]/(X^3) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+25x^52+100x^53+216x^54+342x^55+436x^56+548x^57+645x^58+698x^59+737x^60+764x^61+783x^62+766x^63+625x^64+474x^65+348x^66+226x^67+199x^68+102x^69+42x^70+44x^71+22x^72+26x^73+11x^74+4x^75+3x^76+2x^77+3x^78

The gray image is a linear code over GF(2) with n=244, k=13 and d=104.
This code was found by Heurico 1.16 in 4.07 seconds.