The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1 X^3+X  1  1  1  1  0  1 X^2+X  1  1  1 X^3+X^2  1 X^3+X  1  1  1  0  1 X^3+X  1  1 X^3+X^2  1  1 X^2+X  1  1  1  1  1  1 X^2+X  1  1  1  1  X  1  0  1  1 X^3+X  1  1  1  0  1 X^3 X^3  1  X  1  X  1  0  1  1
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+1  1 X^3+X X^2+X  0 X+1  1 X^2+1  1 X^3+X^2 X^3+X X^3+X^2+X+1  1 X^3+1  1 X^2+X  0 X+1  1 X^2+1  1 X^3+X^2 X^3+X  1 X^3+X^2+X+1 X^3+1  1 X^2+X  0 X^3 X^3+X X^3+X^2 X+1  1 X^2+X X^3+X^2 X^2+X X^3+X^2+X  0 X^2+1  1 X^3+X^2+X+1 X^2  1 X^3+X^2+X  0 X^3+X  1 X^3+X^2+X+1  X  X X^2+X X^2+X X^3+X^2+X X^3+X  X  X X^3+X  0
 0  0 X^3  0  0  0  0  0 X^3 X^3 X^3  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0  0
 0  0  0 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0  0  0  0 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0  0  0  0 X^3 X^3  0 X^3  0
 0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0  0  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0 X^3  0  0  0
 0  0  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0  0  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3  0  0 X^3  0  0  0  0 X^3  0  0  0 X^3 X^3  0 X^3 X^3 X^3 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+38x^62+128x^63+355x^64+236x^65+555x^66+396x^67+744x^68+424x^69+475x^70+232x^71+300x^72+108x^73+75x^74+12x^75+6x^76+6x^78+1x^82+1x^86+2x^92+1x^106

The gray image is a linear code over GF(2) with n=544, k=12 and d=248.
This code was found by Heurico 1.16 in 0.406 seconds.