The generator matrix

 1  0  1  1  1 X^2  X  1  1  1 X^2+X  1  1  1  1  0  1  0  1  1  X  1  1  X  1  1 X^2  1  1 X^2  0 X^2+X  1  1  1  1 X^2 X^2+X  X  X  1  0  1  0 X^2+X  1  1  1  1  1  1 X^2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  1 X^2+X X^2+X+1  1  1 X+1  X X^2+1  1 X^2+X X^2+X X^2 X+1  1 X+1  1 X^2  1  1 X^2  1  1  0 X^2+X+1  1 X^2+X  1  1  1  1 X^2  X X+1 X^2+1  1  1  1  X X^2  0 X^2+X  X  1  1 X^2+X+1 X^2+1 X^2+X+1 X^2 X^2+X  X X^2+1 X^2+1 X^2+X+1 X^2+1  1 X^2+X+1 X+1  1 X^2+1 X^2+X+1 X^2+X+1 X^2+X+1  1  1 X^2+X+1 X+1  0
 0  0  X  0 X^2+X  X  X X^2  X X^2  0  0 X^2+X  X X^2  0  X X^2+X  0 X^2+X  0 X^2+X X^2 X^2+X  0  X  X  0  X X^2+X  0 X^2 X^2+X X^2+X  0 X^2  0 X^2  X X^2+X X^2+X  X X^2 X^2 X^2+X  X X^2  0  X X^2 X^2+X X^2 X^2+X  X X^2  0 X^2  0 X^2  X X^2+X X^2 X^2+X  0 X^2+X X^2+X  X X^2  0
 0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0
 0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0  0 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+23x^64+118x^65+116x^66+102x^67+210x^68+146x^69+42x^70+40x^71+16x^72+68x^73+92x^74+16x^75+12x^77+3x^80+6x^81+3x^82+2x^83+2x^84+2x^85+2x^86+1x^96+1x^98

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 0.249 seconds.