The generator matrix

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

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+418x^72+644x^74+912x^76+584x^78+636x^80+344x^82+286x^84+120x^86+100x^88+36x^90+10x^92+5x^96

The gray image is a linear code over GF(2) with n=312, k=12 and d=144.
This code was found by Heurico 1.16 in 43.4 seconds.