The generator matrix

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

generates a code of length 69 over Z2[X]/(X^4) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+92x^65+616x^66+740x^67+676x^68+554x^69+360x^70+340x^71+240x^72+122x^73+134x^74+76x^75+112x^76+28x^77+1x^78+2x^80+1x^82+1x^84

The gray image is a linear code over GF(2) with n=552, k=12 and d=260.
This code was found by Heurico 1.16 in 2.42 seconds.