The generator matrix

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

generates a code of length 72 over Z2[X]/(X^4) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+91x^66+738x^67+988x^68+1590x^69+1831x^70+2542x^71+1878x^72+2086x^73+1398x^74+1254x^75+744x^76+588x^77+271x^78+230x^79+63x^80+44x^81+25x^82+4x^83+5x^84+10x^85+2x^89+1x^92

The gray image is a linear code over GF(2) with n=576, k=14 and d=264.
This code was found by Heurico 1.16 in 6.77 seconds.