The generator matrix

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

generates a code of length 71 over Z2[X]/(X^4) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+148x^62+800x^63+2458x^64+5302x^65+8682x^66+14296x^67+20532x^68+28634x^69+31735x^70+36504x^71+32994x^72+28102x^73+20593x^74+14722x^75+8258x^76+4602x^77+2179x^78+982x^79+339x^80+164x^81+51x^82+22x^83+22x^84+12x^85+2x^86+2x^87+4x^88+2x^90

The gray image is a linear code over GF(2) with n=568, k=18 and d=248.
This code was found by Heurico 1.16 in 606 seconds.