The generator matrix

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

generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+47x^68+294x^69+391x^70+664x^71+508x^72+780x^73+673x^74+724x^75+564x^76+676x^77+572x^78+528x^79+348x^80+494x^81+237x^82+256x^83+143x^84+126x^85+71x^86+48x^87+21x^88+10x^89+8x^90+4x^91+4x^93

The gray image is a linear code over GF(2) with n=304, k=13 and d=136.
This code was found by Heurico 1.16 in 3.26 seconds.