The generator matrix

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

generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+248x^72+160x^74+296x^76+96x^78+193x^80+8x^84+16x^88+1x^96+4x^104+1x^112

The gray image is a linear code over GF(2) with n=304, k=10 and d=144.
This code was found by Heurico 1.16 in 13.5 seconds.