The generator matrix

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

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+204x^71+191x^72+290x^73+183x^74+262x^75+136x^76+154x^77+100x^78+148x^79+67x^80+92x^81+31x^82+54x^83+40x^84+66x^85+4x^86+4x^87+13x^88+6x^89+1x^90+1x^98

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 0.462 seconds.