The generator matrix

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

generates a code of length 68 over Z2[X]/(X^4) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+92x^62+590x^63+1248x^64+1568x^65+1976x^66+1986x^67+2020x^68+1930x^69+1832x^70+1160x^71+983x^72+460x^73+229x^74+168x^75+50x^76+38x^77+10x^78+30x^79+2x^80+4x^81+5x^82+2x^83

The gray image is a linear code over GF(2) with n=544, k=14 and d=248.
This code was found by Heurico 1.16 in 5.94 seconds.