The generator matrix

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

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+448x^60+1180x^61+2236x^62+2572x^63+3845x^64+4140x^65+4672x^66+3832x^67+3706x^68+2508x^69+1742x^70+836x^71+603x^72+220x^73+108x^74+56x^75+29x^76+16x^77+10x^78+7x^80+1x^84

The gray image is a linear code over GF(2) with n=528, k=15 and d=240.
This code was found by Heurico 1.16 in 13.6 seconds.