The generator matrix

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

generates a code of length 78 over Z2[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+217x^72+284x^73+512x^74+296x^75+489x^76+268x^77+442x^78+248x^79+326x^80+188x^81+206x^82+108x^83+173x^84+76x^85+94x^86+40x^87+60x^88+16x^89+18x^90+12x^91+14x^92+8x^94

The gray image is a linear code over GF(2) with n=312, k=12 and d=144.
This code was found by Heurico 1.11 in 0.422 seconds.