The generator matrix

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

generates a code of length 66 over Z2[X]/(X^4) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+805x^62+768x^63+1220x^64+1080x^65+1216x^66+784x^67+821x^68+480x^69+466x^70+176x^71+250x^72+40x^73+72x^74+10x^76+1x^78+1x^80+1x^84

The gray image is a linear code over GF(2) with n=528, k=13 and d=248.
This code was found by Heurico 1.16 in 121 seconds.