The generator matrix

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

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+236x^62+348x^63+648x^64+624x^65+757x^66+648x^67+730x^68+608x^69+752x^70+476x^71+689x^72+428x^73+414x^74+260x^75+263x^76+152x^77+60x^78+24x^79+34x^80+12x^81+21x^82+4x^83+3x^84

The gray image is a linear code over GF(2) with n=276, k=13 and d=124.
This code was found by Heurico 1.11 in 1.2 seconds.