The generator matrix

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

generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+50x^72+64x^73+24x^74+64x^75+38x^76+8x^78+3x^80+2x^84+2x^88

The gray image is a linear code over GF(2) with n=296, k=8 and d=144.
This code was found by Heurico 1.16 in 0.191 seconds.