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  X  1  0  1  1  1  X  1  1  1  1  1  1  1  1  1 X^3  1  1  1  1  1  1  1  1  1 X^2  1  X  X  1  0  1 X^3+X^2 X^3+X^2  1  1  0  1  0  1  1
 0  X  0 X^3+X^2+X X^2 X^2+X X^3+X^2  X  0 X^2+X X^3 X^2+X X^3+X X^2 X^2  X  0 X^2+X X^2 X^3+X  0 X^3+X  0 X^3+X X^3+X^2+X X^3+X  X X^3+X^2 X^3+X^2 X^3+X^2 X^2+X X^3+X^2 X^3+X  X X^3+X X^2+X X^3+X  X X^3+X^2+X X^3+X  X X^3+X^2 X^3 X^2 X^3+X^2+X X^2+X X^3+X^2+X X^3+X^2 X^2+X X^2+X  X  0 X^2+X  X  X  X X^2  X  X X^3+X^2 X^3+X^2  X X^2+X  X  0 X^3
 0  0 X^3+X^2  0 X^2  0 X^3  0 X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2  0 X^2  0 X^3+X^2 X^3 X^3+X^2 X^2  0 X^2 X^3 X^2 X^2 X^3+X^2 X^2  0 X^2 X^3  0 X^3 X^3 X^3 X^2 X^3+X^2  0 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3  0 X^2 X^3 X^3  0 X^2 X^3+X^2 X^3 X^3+X^2 X^2  0 X^2 X^3  0 X^3 X^3+X^2 X^3 X^3 X^3  0 X^3+X^2  0  0
 0  0  0 X^3+X^2  0 X^3 X^3 X^2 X^2 X^2 X^2  0  0 X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3 X^2 X^3 X^3 X^2  0 X^3 X^2  0  0 X^2  0 X^2 X^3 X^2 X^3+X^2 X^2 X^3+X^2  0 X^2 X^3 X^3+X^2  0 X^2 X^3 X^3 X^3 X^2 X^3  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3  0  0 X^2 X^2 X^3  0  0 X^3 X^2 X^3+X^2
 0  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0 X^3  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+105x^60+84x^61+272x^62+324x^63+350x^64+744x^65+408x^66+744x^67+320x^68+324x^69+204x^70+84x^71+84x^72+18x^74+14x^76+8x^78+5x^80+2x^82+1x^108

The gray image is a linear code over GF(2) with n=528, k=12 and d=240.
This code was found by Heurico 1.16 in 0.687 seconds.