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

generates a code of length 71 over Z2[X]/(X^3) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+142x^66+130x^68+272x^70+230x^72+154x^74+22x^76+54x^78+16x^82+2x^86+1x^128

The gray image is a linear code over GF(2) with n=284, k=10 and d=132.
This code was found by Heurico 1.16 in 66.2 seconds.