The generator matrix

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

generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+130x^67+441x^68+644x^69+1165x^70+1210x^71+1906x^72+1818x^73+2542x^74+2150x^75+3292x^76+2394x^77+3168x^78+2334x^79+2543x^80+1808x^81+1770x^82+1094x^83+981x^84+510x^85+461x^86+154x^87+100x^88+52x^89+38x^90+26x^91+14x^92+4x^93+6x^94+6x^95+2x^96+2x^97+2x^98

The gray image is a linear code over GF(2) with n=308, k=15 and d=134.
This code was found by Heurico 1.16 in 52.8 seconds.