The generator matrix

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

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+55x^60+566x^61+1119x^62+1656x^63+1809x^64+2270x^65+2165x^66+2024x^67+1461x^68+1356x^69+936x^70+544x^71+183x^72+106x^73+47x^74+44x^75+24x^76+6x^77+4x^78+4x^79+3x^80+1x^86

The gray image is a linear code over GF(2) with n=528, k=14 and d=240.
This code was found by Heurico 1.16 in 14.4 seconds.