The generator matrix

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

generates a code of length 72 over Z2[X]/(X^3) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+68x^63+99x^64+264x^65+296x^66+458x^67+618x^68+638x^69+698x^70+676x^71+730x^72+650x^73+746x^74+604x^75+516x^76+390x^77+248x^78+200x^79+60x^80+90x^81+52x^82+34x^83+15x^84+12x^85+6x^86+8x^87+6x^88+4x^89+2x^90+2x^92+1x^100

The gray image is a linear code over GF(2) with n=288, k=13 and d=126.
This code was found by Heurico 1.16 in 5.46 seconds.