The generator matrix

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

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+162x^69+163x^70+364x^71+131x^72+550x^73+201x^74+526x^75+98x^76+480x^77+177x^78+522x^79+93x^80+278x^81+105x^82+98x^83+24x^84+52x^85+14x^86+14x^87+12x^89+6x^90+8x^91+2x^92+2x^93+6x^94+4x^95+2x^96+1x^104

The gray image is a linear code over GF(2) with n=304, k=12 and d=138.
This code was found by Heurico 1.16 in 58.4 seconds.