The generator matrix

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

generates a code of length 69 over Z2[X]/(X^4) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+78x^64+584x^65+1090x^66+1188x^67+1092x^68+972x^69+940x^70+656x^71+474x^72+448x^73+298x^74+196x^75+78x^76+44x^77+40x^78+8x^79+3x^80+2x^84

The gray image is a linear code over GF(2) with n=552, k=13 and d=256.
This code was found by Heurico 1.16 in 10.2 seconds.