The generator matrix

 1  0  1  1  1  0  1  1  X  1 X^2+X  1  1  1  0  1  1 X^2  1  1  X  1  1 X^2+X X^2+X  1 X^2 X^2+X  1  1  1  0  1  1  1  1  0  1  1  0  1  X  1  1  1  1 X^2+X  1  1  1  0  X  1  1  0  1  1  1  1  0 X^2  1  1  X  X  1  0 X^2+X  1 X^2 X^2  1
 0  1  1  0 X+1  1  X X^2+X+1  1 X^2+X  1 X^2+1  0 X+1  1 X^2 X^2+X+1  1  X X^2+1  1 X^2+X  1  1  1  0  1  1 X^2+X+1 X^2  X  1 X^2+1 X+1  0  X  1 X^2+X+1 X^2+1  1 X^2+1  1  0 X^2+X  1  0  1 X^2+X+1 X+1 X^2  1  1  0 X^2  0 X^2 X+1 X^2+X  0  1  1 X^2+1 X+1  X X^2 X^2  1  1 X^2+1  1  1  0
 0  0  X X^2+X  0 X^2+X  X X^2+X  X  0 X^2  0 X^2  0  0  X  X X^2+X  X  0  X X^2  X X^2  0  0  X  X X^2+X  X  X X^2  0  0  X  X X^2  0  0  0  0 X^2+X X^2  0  X  0  0 X^2+X X^2+X X^2  X X^2+X  X X^2  X  0 X^2 X^2  X X^2  X X^2 X^2+X  X  X  0 X^2+X  0  0  X  X  0
 0  0  0 X^2  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0
 0  0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0
 0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0
 0  0  0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0
 0  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0  0  0  0 X^2  0
 0  0  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 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+24x^60+56x^61+115x^62+144x^63+283x^64+536x^65+473x^66+926x^67+676x^68+1620x^69+920x^70+1840x^71+1141x^72+1946x^73+1046x^74+1500x^75+661x^76+1008x^77+399x^78+384x^79+220x^80+188x^81+89x^82+54x^83+42x^84+20x^85+22x^86+16x^87+17x^88+2x^89+8x^90+5x^92+2x^96

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 17.6 seconds.