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

generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+109x^68+280x^69+425x^70+474x^71+529x^72+740x^73+748x^74+626x^75+691x^76+652x^77+611x^78+602x^79+425x^80+372x^81+310x^82+212x^83+142x^84+92x^85+63x^86+34x^87+20x^88+8x^89+18x^90+2x^91+2x^92+1x^94+2x^95+1x^96

The gray image is a linear code over GF(2) with n=304, k=13 and d=136.
This code was found by Heurico 1.16 in 4.28 seconds.