The generator matrix

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

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+29x^72+80x^73+28x^74+96x^75+16x^77+2x^78+1x^80+1x^88+2x^94

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.