The generator matrix

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

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+44x^61+293x^62+336x^63+541x^64+542x^65+726x^66+628x^67+813x^68+678x^69+774x^70+544x^71+668x^72+338x^73+444x^74+312x^75+244x^76+110x^77+53x^78+32x^79+28x^80+8x^81+14x^82+4x^83+7x^84+8x^85+2x^88

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 3.41 seconds.