The generator matrix

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

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+117x^60+8x^61+353x^62+24x^63+697x^64+128x^65+897x^66+332x^67+1389x^68+596x^69+1801x^70+928x^71+1925x^72+976x^73+1807x^74+648x^75+1307x^76+320x^77+876x^78+104x^79+509x^80+16x^81+339x^82+12x^83+168x^84+4x^85+65x^86+27x^88+5x^90+2x^92+1x^94+1x^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 23.4 seconds.