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  1  1  1  1  1  1  1  1  0  0  0 X^2 X^2  X X^2  X X^2  0  X  X  X  1 X^2  X  0  X  0  1 X^2  1  X X^2  1  1
 0  X  0  0  0  0  0  0  0  0 X^2  X  X X^2+X  0 X^2+X X^2+X  0  X X^2 X^2+X X^2  X  X  X X^2  X  0  X X^2 X^2+X  X X^2+X X^2+X X^2+X X^2+X  X X^2  0 X^2+X X^2+X X^2  X X^2+X  X  0 X^2  X  0  X X^2 X^2+X  X  0  X  X X^2  0  X X^2+X  X  X  X X^2  0 X^2+X  0 X^2  0  X  0 X^2
 0  0  X  0  0  0  0  0  0  0 X^2+X X^2  X  X  X  X  0  X  0  X X^2+X X^2  0 X^2+X  X  X X^2+X X^2+X X^2  0 X^2+X  0 X^2 X^2+X  X  0 X^2 X^2  X  0 X^2  X X^2+X X^2+X  X  X  0 X^2  X X^2 X^2 X^2+X  0 X^2 X^2 X^2+X X^2 X^2+X  0  X  0 X^2+X X^2+X X^2+X  X  0 X^2 X^2+X X^2+X X^2+X X^2 X^2
 0  0  0  X  0  0  0  X X^2+X  X  X X^2+X  0  X X^2  0 X^2+X X^2+X X^2+X X^2 X^2+X  X  0 X^2  0 X^2  X  X  X X^2  X  0 X^2+X  0  X X^2+X  0 X^2  X  X X^2 X^2+X  0 X^2  X  0  0  X X^2  X X^2 X^2+X X^2  0 X^2 X^2+X  0 X^2 X^2  X  0  X X^2  0 X^2+X  0  X  X  X X^2  0 X^2
 0  0  0  0  X  0  X  X  X X^2  X  X  X X^2 X^2 X^2+X X^2+X X^2 X^2 X^2+X X^2+X  X X^2+X X^2 X^2  X  0 X^2+X X^2 X^2+X X^2+X  X X^2+X  X  0 X^2+X X^2+X  0  0 X^2  X X^2  0 X^2+X X^2 X^2  X X^2  0 X^2+X  X X^2+X  X X^2  X  0  X X^2+X  X X^2+X X^2+X  0 X^2+X X^2+X  X X^2  X X^2+X  0 X^2+X X^2+X X^2
 0  0  0  0  0  X  X X^2 X^2+X X^2+X  X  X X^2+X  0  X X^2 X^2 X^2 X^2+X  X  0 X^2 X^2  0  X  0  X X^2 X^2 X^2+X X^2+X X^2+X X^2+X  0 X^2 X^2 X^2 X^2  0  0 X^2+X X^2+X X^2+X X^2+X  X  X X^2  X X^2  X  X  X  0  X X^2 X^2 X^2+X  0 X^2+X X^2  X X^2+X X^2  0  0 X^2 X^2  X X^2  X  0  X
 0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2  0  0 X^2  0  0  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+37x^60+122x^61+214x^62+290x^63+339x^64+500x^65+601x^66+736x^67+892x^68+1064x^69+1231x^70+1390x^71+1558x^72+1454x^73+1338x^74+1030x^75+853x^76+796x^77+530x^78+372x^79+320x^80+226x^81+149x^82+130x^83+82x^84+58x^85+32x^86+20x^87+14x^88+4x^89+1x^102

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 23.8 seconds.