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

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+106x^62+20x^63+191x^64+108x^65+160x^66+224x^67+111x^68+312x^69+104x^70+244x^71+89x^72+92x^73+96x^74+24x^75+83x^76+34x^78+34x^80+8x^82+2x^84+4x^86+1x^112

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 0.465 seconds.