The generator matrix

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

generates a code of length 67 over Z2[X]/(X^4) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+516x^61+1099x^62+2172x^63+2885x^64+3850x^65+4026x^66+4398x^67+3738x^68+3746x^69+2731x^70+1700x^71+891x^72+558x^73+198x^74+150x^75+32x^76+50x^77+8x^78+12x^79+5x^80+2x^82

The gray image is a linear code over GF(2) with n=536, k=15 and d=244.
This code was found by Heurico 1.16 in 34.2 seconds.