The generator matrix

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

generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+135x^64+200x^65+322x^66+152x^67+306x^68+172x^69+204x^70+80x^71+109x^72+80x^73+83x^74+48x^75+66x^76+20x^77+18x^78+8x^79+19x^80+8x^81+13x^82+2x^84+2x^88

The gray image is a linear code over GF(2) with n=276, k=11 and d=128.
This code was found by Heurico 1.16 in 0.324 seconds.