The generator matrix

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

generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+232x^69+400x^70+668x^71+630x^72+790x^73+639x^74+820x^75+584x^76+656x^77+427x^78+580x^79+389x^80+428x^81+263x^82+228x^83+154x^84+144x^85+61x^86+40x^87+32x^88+22x^89+2x^90+2x^92

The gray image is a linear code over GF(2) with n=304, k=13 and d=138.
This code was found by Heurico 1.11 in 1.34 seconds.