The generator matrix

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

generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+118x^69+44x^70+94x^72+98x^73+112x^74+128x^75+248x^76+356x^77+316x^78+128x^79+137x^80+76x^81+16x^82+8x^84+102x^85+20x^86+21x^88+18x^89+4x^94+2x^96+1x^136

The gray image is a linear code over GF(2) with n=308, k=11 and d=138.
This code was found by Heurico 1.16 in 28.3 seconds.