The generator matrix

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

generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+100x^66+230x^67+430x^68+444x^69+662x^70+572x^71+897x^72+668x^73+719x^74+558x^75+660x^76+448x^77+536x^78+356x^79+357x^80+194x^81+138x^82+66x^83+76x^84+34x^85+18x^86+8x^87+9x^88+2x^89+3x^90+2x^91+2x^92+2x^93

The gray image is a linear code over GF(2) with n=296, k=13 and d=132.
This code was found by Heurico 1.16 in 4.21 seconds.