The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  X  1  1  1  1 X^2  1  X
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2 X^3  0  0 X^2 X^3+X^2 X^2  0 X^2 X^3 X^3+X^2  0 X^3 X^3+X^2 X^3  0 X^3 X^2  0 X^3+X^2 X^3+X^2  0 X^2 X^2 X^3+X^2 X^3+X^2 X^3  0 X^3+X^2 X^3+X^2 X^3 X^2 X^2 X^2 X^2 X^3  0  0 X^3  0 X^3+X^2 X^3+X^2 X^3+X^2
 0  0 X^3+X^2  0 X^2 X^2 X^2 X^3  0 X^3 X^2 X^3+X^2 X^2 X^2 X^3 X^3  0 X^3+X^2  0 X^2  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3 X^2  0 X^3+X^2  0  0 X^3+X^2 X^3 X^2 X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^2 X^2  0 X^3 X^3+X^2 X^3+X^2 X^2  0 X^3  0 X^2 X^3+X^2 X^2 X^3  0 X^3  0 X^3 X^3+X^2 X^3  0 X^3 X^2 X^2 X^3 X^2
 0  0  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^3+X^2 X^2  0 X^3+X^2  0 X^3 X^3+X^2 X^2  0 X^3+X^2  0 X^2 X^3 X^2 X^2 X^3  0 X^3+X^2 X^3+X^2 X^3  0  0 X^3 X^3+X^2 X^3  0 X^2 X^3+X^2 X^2  0  0 X^3+X^2 X^3+X^2  0 X^2 X^2 X^3 X^3 X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3  0 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^2  0 X^2
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0  0  0  0  0 X^3 X^3  0 X^3 X^3  0  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 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 60.

Homogenous weight enumerator: w(x)=1x^0+65x^60+90x^62+32x^63+85x^64+480x^65+568x^66+480x^67+70x^68+32x^69+68x^70+58x^72+8x^74+8x^76+2x^78+1x^124

The gray image is a linear code over GF(2) with n=528, k=11 and d=240.
This code was found by Heurico 1.16 in 0.359 seconds.