The generator matrix

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

generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+212x^71+134x^72+380x^73+110x^74+304x^75+107x^76+226x^77+40x^78+166x^79+48x^80+96x^81+38x^82+80x^83+19x^84+34x^85+4x^86+34x^87+9x^88+4x^91+2x^92

The gray image is a linear code over GF(2) with n=304, k=11 and d=142.
This code was found by Heurico 1.11 in 5.91 seconds.