The generator matrix

 1  0  0  0  1  1  1  1 X^2  1 X^2+X  X  1 X^2  1  1  X  1  1  0  1 X^2+X  X  X X^2+X  1  1  1  0  X  1  1  1 X^2+X  1 X^2  1 X^2  0  1  1 X^2+X X^2  0  1  1  1 X^2+X X^2  1  1  1  1  1  1  1 X^2+X X^2  1  X  1  1  1  1  X X^2+X  1  X  1  1  1  0  1  X  1
 0  1  0  0  0 X^2  1 X^2+1  1 X^2+X+1 X^2  1  0  1 X+1 X^2+1  1 X^2+X  0  X  1  1 X^2+X  1  0  X X^2  1  X  1  1  X  X  X X^2+X+1  1  X  1  X X^2+1  0  1  0 X^2  X X^2+1 X+1  1 X^2 X+1  0 X^2+X X^2+X+1 X+1  0 X^2  1  0  0  X  X X+1  1 X^2  1 X^2 X^2+X+1 X^2+X X+1 X^2 X^2  X X^2+X  1  0
 0  0  1  0  0 X^2+1  1 X^2+X X+1 X^2+1  1 X^2 X^2+X+1 X^2+1 X^2  0 X^2 X^2+1 X+1  1 X+1 X+1 X^2+X  X  1 X^2  1 X^2+X+1  0  1 X^2 X^2  X  1 X^2+X X^2+X  X X^2+1  1  1 X+1 X^2+X  1  0  1 X^2+1 X^2+X  0  1 X^2+X+1 X^2+1 X^2+X+1  X X+1 X^2+X+1 X^2+X  1  X X^2+X+1  1  0 X^2+X  X  X X+1  1 X^2+X  1  0 X^2+X+1 X+1  X X^2+1 X^2+X  0
 0  0  0  1  1  1 X^2 X+1 X+1 X^2+1 X^2+1 X^2+1  X  X X^2 X^2+X+1  0 X^2+1  0  0 X^2+1  1  1 X+1 X+1 X^2+X X+1 X^2  1 X^2+X  X X^2+X+1 X^2+X  X X^2+X+1 X^2+X X+1 X+1  0  0  1 X^2+1 X+1  1 X^2 X^2+X X^2+X+1 X^2+X+1 X^2+1 X^2+1  0 X+1 X^2 X+1 X^2+X+1  X X^2+X  1 X^2  0 X^2+X+1 X+1 X^2+1 X^2+1  1 X^2 X^2+X+1 X^2+1 X^2+X X^2+X X^2  1  1 X^2 X^2
 0  0  0  0  X  0  0  0  0  X  X  X X^2+X  X  X X^2 X^2  0 X^2+X X^2 X^2 X^2+X  X X^2 X^2  X X^2+X  X X^2  0  0 X^2+X X^2+X  X X^2+X X^2+X  0 X^2 X^2+X  X  0 X^2  0  X X^2 X^2  X X^2 X^2+X  0 X^2+X X^2+X  0 X^2  X  X X^2+X  X X^2 X^2+X  0  0  0 X^2+X  0  X X^2 X^2  0  X  0 X^2 X^2+X  0 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+80x^66+322x^67+648x^68+718x^69+884x^70+1206x^71+1153x^72+1206x^73+1427x^74+1338x^75+1358x^76+1396x^77+1100x^78+932x^79+779x^80+690x^81+487x^82+248x^83+205x^84+98x^85+50x^86+28x^87+13x^88+4x^89+4x^90+4x^91+3x^92+2x^95

The gray image is a linear code over GF(2) with n=300, k=14 and d=132.
This code was found by Heurico 1.13 in 4.53 seconds.