The generator matrix

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

generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+239x^62+382x^63+632x^64+608x^65+709x^66+572x^67+882x^68+580x^69+724x^70+574x^71+626x^72+464x^73+376x^74+240x^75+244x^76+126x^77+117x^78+24x^79+45x^80+12x^81+11x^82+2x^84+2x^85

The gray image is a linear code over GF(2) with n=276, k=13 and d=124.
This code was found by Heurico 1.16 in 3.04 seconds.