The generator matrix

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

generates a code of length 67 over Z2[X]/(X^4) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+140x^63+662x^64+598x^65+746x^66+424x^67+471x^68+262x^69+254x^70+212x^71+169x^72+48x^73+85x^74+12x^75+8x^76+2x^78+1x^80+1x^86

The gray image is a linear code over GF(2) with n=536, k=12 and d=252.
This code was found by Heurico 1.16 in 1 seconds.