The generator matrix

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

generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+86x^67+111x^68+252x^69+448x^70+458x^71+526x^72+594x^73+647x^74+710x^75+756x^76+740x^77+597x^78+510x^79+520x^80+360x^81+285x^82+232x^83+100x^84+84x^85+50x^86+40x^87+27x^88+14x^89+16x^90+12x^91+5x^92+4x^93+4x^94+2x^96+1x^102

The gray image is a linear code over GF(2) with n=304, k=13 and d=134.
This code was found by Heurico 1.16 in 4.86 seconds.