The generator matrix

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

generates a code of length 66 over Z2[X]/(X^4) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+178x^59+1132x^60+2650x^61+3895x^62+5628x^63+7232x^64+8210x^65+8341x^66+8266x^67+6911x^68+5350x^69+3737x^70+2146x^71+1031x^72+466x^73+187x^74+92x^75+45x^76+24x^77+10x^79+4x^81

The gray image is a linear code over GF(2) with n=528, k=16 and d=236.
This code was found by Heurico 1.16 in 34 seconds.