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  1  1 X^2+X  1  1  1  0  1  0  1  1  X  1  1 X^2 X^2+X  1 X^2+X  1  1  0 X^2+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^2+1 X^2 X^2+X+1 X^2+X  1 X^2+1  X X^2+X  X X^2+X X^2 X^2+X X+1  1  1 X+1  X  1  0  1  X  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+1 X^2+1 X^2+X X^2  X X^2+1 X^2  1 X+1  1 X^2+X X^2 X^2  0  0  1  X X+1 X^2+1  X X+1  1 X^2+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 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2
 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  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  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  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0
 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 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0  0  0 X^2 X^2  0  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+72x^68+270x^69+351x^70+638x^71+551x^72+778x^73+599x^74+756x^75+602x^76+764x^77+544x^78+510x^79+404x^80+430x^81+243x^82+300x^83+145x^84+116x^85+36x^86+26x^87+16x^88+8x^89+18x^90+8x^91+1x^92+2x^93+1x^94+2x^95

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 4.57 seconds.