The generator matrix

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

generates a code of length 72 over Z2[X]/(X^4) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+144x^63+962x^64+2594x^65+5113x^66+8772x^67+14776x^68+20880x^69+27057x^70+32618x^71+35729x^72+32798x^73+28444x^74+21136x^75+14208x^76+8334x^77+4503x^78+2236x^79+1108x^80+450x^81+153x^82+68x^83+30x^84+14x^85+10x^86+2x^87+2x^88+2x^89

The gray image is a linear code over GF(2) with n=576, k=18 and d=252.
This code was found by Heurico 1.16 in 613 seconds.