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

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+119x^66+4x^67+227x^68+56x^69+343x^70+88x^71+423x^72+232x^73+487x^74+272x^75+501x^76+200x^77+368x^78+136x^79+249x^80+24x^81+148x^82+12x^83+95x^84+49x^86+31x^88+21x^90+7x^92+1x^98+1x^100+1x^116

The gray image is a linear code over GF(2) with n=300, k=12 and d=132.
This code was found by Heurico 1.16 in 1.75 seconds.