The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1 X^2+X  1  1  1  0  1  1 X^2+X  1  1  0  1  1 X^2+X X^2  1  1  X  1  1  1  1 X^2+X  1  1  0  1  1  0  1  1 X^2+X  1  1 X^2  1  1  X  X  X  1  1  X  X  1  1  0 X^2  1  X  1  1  1  1  1  X  X  X X^2
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X  1 X^2+1 X+1  0  1 X^2+X X^2+1  1 X^2 X^2+X+1  1  X X^2+1  1  1  0 X+1  1 X^2+X X^2+1  0 X+1  1 X^2+X X^2+1  1  0 X+1  1 X^2+X X^2+1  1 X^2 X^2+X+1  1  X  1  1  0 X^2  0 X^2 X^2+X  X X^2+1  1  X  X X^2+X  0 X^2 X^2  0 X^2+X X^2  0 X^2+X  X  0
 0  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  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  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2  0  0  0
 0  0  0  0 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2  0
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0 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 X^2 X^2  0 X^2 X^2 X^2 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 64.

Homogenous weight enumerator: w(x)=1x^0+163x^64+178x^66+208x^68+128x^70+203x^72+106x^74+22x^76+4x^78+9x^80+1x^84+1x^124

The gray image is a linear code over GF(2) with n=276, k=10 and d=128.
This code was found by Heurico 1.16 in 0.214 seconds.