The generator matrix

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

generates a code of length 75 over Z2[X]/(X^3) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+34x^66+34x^67+70x^68+78x^69+88x^70+114x^71+133x^72+174x^73+211x^74+226x^75+203x^76+202x^77+121x^78+98x^79+59x^80+42x^81+36x^82+36x^83+36x^84+16x^85+10x^86+4x^87+7x^88+7x^90+3x^92+4x^94+1x^126

The gray image is a linear code over GF(2) with n=300, k=11 and d=132.
This code was found by Heurico 1.16 in 0.684 seconds.