The generator matrix

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

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+51x^66+280x^67+355x^68+610x^69+571x^70+764x^71+588x^72+746x^73+600x^74+732x^75+582x^76+680x^77+398x^78+426x^79+215x^80+194x^81+153x^82+120x^83+41x^84+36x^85+19x^86+8x^87+6x^88+4x^89+4x^91+2x^92+2x^93+2x^95+2x^96

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 3.76 seconds.