The generator matrix

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

generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+20x^73+70x^74+24x^75+1x^76+6x^78+1x^80+4x^81+1x^84

The gray image is a linear code over GF(2) with n=296, k=7 and d=146.
This code was found by Heurico 1.16 in 0.236 seconds.