The generator matrix

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

generates a code of length 72 over Z2[X]/(X^3) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+104x^60+8x^61+88x^62+44x^63+481x^64+284x^65+492x^66+712x^67+1009x^68+1200x^69+1260x^70+1816x^71+1477x^72+1912x^73+1120x^74+1232x^75+1023x^76+616x^77+536x^78+284x^79+350x^80+76x^81+84x^82+8x^83+100x^84+4x^86+41x^88+19x^92+2x^96+1x^100

The gray image is a linear code over GF(2) with n=288, k=14 and d=120.
This code was found by Heurico 1.16 in 17.7 seconds.