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

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+154x^62+120x^63+330x^64+216x^65+504x^66+212x^67+265x^68+64x^69+87x^70+16x^71+59x^72+8x^73+6x^74+4x^75+1x^78+1x^116

The gray image is a linear code over GF(2) with n=528, k=11 and d=248.
This code was found by Heurico 1.16 in 0.328 seconds.