The generator matrix

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

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+264x^70+146x^71+649x^72+236x^73+544x^74+198x^75+480x^76+158x^77+395x^78+132x^79+325x^80+66x^81+194x^82+38x^83+113x^84+34x^85+63x^86+14x^87+31x^88+2x^89+12x^90+1x^92

The gray image is a linear code over GF(2) with n=304, k=12 and d=140.
This code was found by Heurico 1.11 in 0.422 seconds.