The generator matrix

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

generates a code of length 66 over Z2[X]/(X^4) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+112x^61+205x^62+500x^63+475x^64+572x^65+475x^66+562x^67+422x^68+442x^69+167x^70+80x^71+43x^72+22x^73+1x^74+2x^75+2x^77+4x^79+2x^81+4x^83+2x^84+1x^88

The gray image is a linear code over GF(2) with n=528, k=12 and d=244.
This code was found by Heurico 1.16 in 0.469 seconds.