The generator matrix

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

generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+178x^71+202x^72+302x^73+182x^74+256x^75+132x^76+206x^77+99x^78+140x^79+44x^80+80x^81+44x^82+62x^83+28x^84+30x^85+27x^86+16x^87+7x^88+6x^89+2x^91+2x^92+2x^95

The gray image is a linear code over GF(2) with n=304, k=11 and d=142.
This code was found by Heurico 1.16 in 0.501 seconds.