The generator matrix

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

generates a code of length 70 over Z2[X]/(X^4) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+66x^66+334x^67+234x^68+352x^69+166x^70+354x^71+133x^72+268x^73+76x^74+30x^75+24x^76+4x^77+2x^79+2x^86+1x^90+1x^106

The gray image is a linear code over GF(2) with n=560, k=11 and d=264.
This code was found by Heurico 1.16 in 0.375 seconds.