The generator matrix

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

generates a code of length 73 over Z2[X]/(X^4) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+102x^66+632x^67+1202x^68+2340x^69+2551x^70+3868x^71+3917x^72+4376x^73+3484x^74+3764x^75+2333x^76+2024x^77+1023x^78+592x^79+292x^80+144x^81+41x^82+36x^83+22x^84+12x^85+6x^86+4x^87+1x^90+1x^92

The gray image is a linear code over GF(2) with n=584, k=15 and d=264.
This code was found by Heurico 1.16 in 14 seconds.