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

generates a code of length 68 over Z2[X]/(X^4) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+106x^63+305x^64+434x^65+487x^66+558x^67+502x^68+466x^69+475x^70+356x^71+204x^72+84x^73+61x^74+20x^75+8x^76+4x^77+1x^78+10x^79+2x^80+2x^81+6x^83+2x^84+2x^85

The gray image is a linear code over GF(2) with n=544, k=12 and d=252.
This code was found by Heurico 1.16 in 0.656 seconds.