The generator matrix

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

generates a code of length 65 over Z2[X]/(X^3) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+277x^56+492x^57+1040x^58+1160x^59+1755x^60+1972x^61+2612x^62+2504x^63+2981x^64+3056x^65+3172x^66+2628x^67+2709x^68+1996x^69+1598x^70+1040x^71+842x^72+412x^73+274x^74+92x^75+96x^76+8x^77+32x^78+11x^80+6x^82+2x^86

The gray image is a linear code over GF(2) with n=260, k=15 and d=112.
This code was found by Heurico 1.16 in 43.4 seconds.