The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  1  1  1  1  1  1  1  1  X  X  1 X^2  1  1  0  1  0  X  1  1  X  1  1  X  1  1  1  X
 0  X  0  0  0  X X^2+X  X X^2 X^2  X  0  0  X  X X^2+X  0  0 X^2+X  X X^2  X X^2+X  X X^2  0 X^2 X^2 X^2+X  0  X X^2+X  X X^2+X X^2+X  X  0 X^2 X^2+X  X  0  0 X^2  0 X^2 X^2  0  0  X X^2+X X^2 X^2+X  0 X^2+X X^2+X X^2 X^2+X  0  X  0 X^2+X X^2 X^2+X X^2+X  X X^2  0  0 X^2+X
 0  0  X  0  X  X  X  0 X^2  0 X^2+X  X X^2+X  0 X^2+X  0 X^2 X^2+X X^2 X^2+X  0 X^2  X  0 X^2+X X^2+X  X X^2  X X^2  0 X^2+X  X  X  0 X^2  0 X^2+X X^2 X^2  0  X X^2+X  0  0 X^2+X X^2+X  0 X^2 X^2  X X^2+X  X  X X^2 X^2  0  0  X X^2+X X^2  0  0 X^2+X  X  X  X X^2 X^2+X
 0  0  0  X  X  0  X X^2+X  0  X X^2  X X^2 X^2+X  X  0 X^2  X  X  0 X^2+X X^2 X^2+X X^2+X  0  0 X^2+X  X  X  0  0  0  0  0 X^2 X^2 X^2  X X^2 X^2  X  0 X^2+X X^2+X X^2 X^2+X  X X^2 X^2+X X^2 X^2  0  X  0 X^2+X  X  0  X  0 X^2+X  0 X^2+X  X X^2  0  X X^2  0  X
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2  0 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  0  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0
 0  0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  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+129x^62+180x^64+56x^65+220x^66+128x^67+294x^68+160x^69+253x^70+112x^71+193x^72+40x^73+99x^74+16x^75+71x^76+62x^78+22x^80+5x^82+6x^84+1x^116

The gray image is a linear code over GF(2) with n=276, k=11 and d=124.
This code was found by Heurico 1.16 in 0.597 seconds.