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

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+68x^63+213x^64+628x^65+501x^66+496x^67+440x^68+506x^69+431x^70+440x^71+148x^72+144x^73+40x^74+18x^75+7x^76+2x^77+1x^78+4x^80+2x^82+2x^83+2x^88+1x^90+1x^92

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 0.438 seconds.