The generator matrix

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

generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+68x^61+217x^62+376x^63+470x^64+656x^65+684x^66+664x^67+783x^68+750x^69+704x^70+626x^71+561x^72+430x^73+361x^74+332x^75+213x^76+122x^77+58x^78+44x^79+20x^80+18x^81+19x^82+4x^83+4x^85+1x^86+2x^87+4x^90

The gray image is a linear code over GF(2) with n=276, k=13 and d=122.
This code was found by Heurico 1.16 in 3.37 seconds.