The generator matrix

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

generates a code of length 67 over Z2[X]/(X^4) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+109x^62+478x^63+1211x^64+1060x^65+1122x^66+996x^67+992x^68+628x^69+565x^70+310x^71+376x^72+200x^73+84x^74+36x^75+12x^76+5x^78+4x^79+2x^82+1x^86

The gray image is a linear code over GF(2) with n=536, k=13 and d=248.
This code was found by Heurico 1.16 in 2.03 seconds.