The generator matrix

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

generates a code of length 75 over Z2[X]/(X^3) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+98x^69+171x^70+208x^71+206x^72+176x^73+152x^74+138x^75+172x^76+154x^77+154x^78+130x^79+107x^80+74x^81+44x^82+26x^83+5x^84+3x^86+6x^87+2x^88+6x^89+4x^90+4x^91+2x^92+4x^93+1x^100

The gray image is a linear code over GF(2) with n=300, k=11 and d=138.
This code was found by Heurico 1.16 in 0.508 seconds.