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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X
 0  X  0  X  0 X^3 X^3+X  X X^2 X^2+X X^2 X^3+X^2+X X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X  0 X^3+X^2  X X^3+X^2+X  X  0 X^3 X^3+X X^2  0 X^2+X X^3+X X^2 X^3+X^2+X X^2+X  0 X^2  X X^3+X  X  0 X^3  0 X^3+X^2+X  X X^2 X^3+X^2 X^3  X X^3+X^2+X X^3 X^3+X X^2 X^3+X^2 X^2+X X^3+X^2+X X^3+X^2 X^2 X^3+X^2+X X^2+X X^3+X^2 X^2  0 X^3 X^2+X X^3+X^2+X X^3+X  X X^2 X^3+X^2
 0  0  X  X X^3+X^2 X^3+X^2+X X^2+X X^2 X^2 X^3+X^2+X  X  0 X^3 X^3+X^2+X X^3+X X^2  0 X^3+X  X X^2 X^3+X^2+X  X X^3+X^2 X^3+X^2 X^2 X^2+X X^3+X^2+X X^3 X^2+X X^3+X X^3 X^3 X^3 X^3+X X^2 X^2 X^3+X X^2  X X^3+X^2 X^3+X^2+X  X  X X^3 X^2+X X^2 X^2 X^3+X X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X X^3 X^3  X  X X^2+X X^2+X X^3+X^2+X X^3+X^2+X  0  0 X^3 X^3  X X^3+X
 0  0  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0  0  0  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0  0  0
 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  0 X^3 X^3 X^3  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3  0  0  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3  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+768x^62+254x^64+2048x^66+256x^68+768x^70+1x^128

The gray image is a linear code over GF(2) with n=528, k=12 and d=248.
This code was found by Heurico 1.16 in 0.563 seconds.