The generator matrix

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

generates a code of length 70 over Z2[X]/(X^4) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+156x^65+272x^66+440x^67+520x^68+540x^69+427x^70+428x^71+474x^72+366x^73+297x^74+82x^75+38x^76+24x^77+8x^78+8x^79+6x^80+1x^82+1x^86+1x^88+2x^89+2x^91+2x^94

The gray image is a linear code over GF(2) with n=560, k=12 and d=260.
This code was found by Heurico 1.16 in 0.891 seconds.