The generator matrix

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

generates a code of length 69 over Z2[X]/(X^4) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+67x^60+796x^61+2341x^62+4910x^63+8839x^64+13820x^65+20913x^66+27638x^67+33155x^68+36294x^69+33803x^70+28706x^71+21233x^72+13500x^73+8243x^74+4390x^75+2042x^76+832x^77+348x^78+144x^79+67x^80+32x^81+16x^82+4x^83+4x^84+6x^85

The gray image is a linear code over GF(2) with n=552, k=18 and d=240.
This code was found by Heurico 1.16 in 597 seconds.