The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  X  1 X^3  1  1 X^2  1  1  1 X^2+X  1  1 X^3+X^2  1 X^3+X  1  1  1  1  1 X^3+X  1  0  1  1  1  1  1 X^3 X^3+X^2+X  1  1  1  1  1 X^3  X X^2  1  1 X^2+X  1  1  X  1  1  1  1  1  1  1  1  1  1  1  X  X  1 X^2  1  1  1
 0  1 X+1 X^2+X X^3+X^2+1  1 X^3+X^2  1 X^2+X+1  1 X^3+X  1  1 X^3 X+1 X^3+X^2+X  1 X^3+X^2+X+1 X^2  1  X  1 X+1 X^3+X^2+X+1 X^2+1 X^3+1  0  1 X^2+1  1 X^3+X^2+X X^3+X+1 X^2 X^3+X^2+1 X^2+X  1  1 X^3+1 X^3+X^2 X^3+X X^2+X X^3+X+1  1  1  1 X^3  1  1  0  X X^2 X^3+X X^3 X^2 X^3+X^2 X^3+X  X X^2 X^2 X^3+X X^2+X X^3+X^2+X X^2+X X^3+X^2 X^3  1 X^3+X^2+1 X^2+1 X^3
 0  0 X^2  0 X^3+X^2 X^2  0 X^2 X^3+X^2 X^3+X^2  0 X^2 X^3+X^2 X^2 X^3 X^3+X^2  0 X^3 X^2  0 X^3+X^2  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3+X^2 X^2 X^2 X^3+X^2 X^3 X^2 X^2  0  0 X^3 X^2 X^2 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3 X^2 X^2  0 X^3  0  0 X^3  0 X^2 X^3 X^3 X^2 X^2 X^3 X^2 X^3  0  0
 0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3
 0  0  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3  0  0  0  0 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+108x^64+274x^65+378x^66+558x^67+551x^68+594x^69+410x^70+466x^71+332x^72+244x^73+93x^74+26x^75+29x^76+6x^77+12x^78+2x^79+2x^81+2x^82+4x^83+2x^84+1x^96+1x^98

The gray image is a linear code over GF(2) with n=552, k=12 and d=256.
This code was found by Heurico 1.16 in 0.516 seconds.