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  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1
 0  X  0 X^2+X X^2 X^3+X^2+X X^3+X^2  X  0 X^2+X X^3+X^2 X^3+X  0 X^3+X^2+X X^2  X X^3+X^2+X  0  0 X^2+X X^3+X X^2 X^3+X^2  X  X X^3 X^2+X X^2 X^3+X^2+X X^3 X^3+X^2 X^3+X  X  0 X^3 X^3+X^2+X X^3+X X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X X^3  0 X^2+X X^3+X X^3+X X^2 X^2 X^3  X X^2 X^2+X X^3 X^3+X^2+X X^3+X^2 X^3+X X^3 X^2+X X^2  X X^3 X^2+X X^3+X^2 X^3+X  0 X^2+X X^2+X X^3  0
 0  0 X^3+X^2  0 X^3+X^2 X^2  0 X^2 X^3 X^3 X^3 X^3 X^2 X^3+X^2 X^2 X^3+X^2 X^2  0 X^3+X^2  0  0 X^3+X^2  0 X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^3 X^2 X^2 X^3 X^3 X^3 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3 X^3+X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^3 X^3 X^3 X^3+X^2 X^2  0 X^2 X^2  0 X^3  0  0 X^3+X^2 X^2 X^3+X^2 X^3+X^2  0  0  0 X^2 X^3
 0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3

generates a code of length 69 over Z2[X]/(X^4) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+8x^66+26x^67+182x^68+590x^69+184x^70+22x^71+8x^72+2x^73+1x^136

The gray image is a linear code over GF(2) with n=552, k=10 and d=264.
This code was found by Heurico 1.16 in 0.437 seconds.