The generator matrix

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

generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+212x^70+284x^71+407x^72+430x^73+442x^74+332x^75+442x^76+244x^77+281x^78+170x^79+206x^80+162x^81+148x^82+76x^83+72x^84+56x^85+69x^86+30x^87+8x^88+4x^89+16x^90+4x^91

The gray image is a linear code over GF(2) with n=304, k=12 and d=140.
This code was found by Heurico 1.16 in 0.962 seconds.