The generator matrix

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

generates a code of length 78 over Z2[X]/(X^3) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+140x^67+524x^68+926x^69+1476x^70+1958x^71+2715x^72+3164x^73+4059x^74+4436x^75+5344x^76+5188x^77+5526x^78+5394x^79+5411x^80+4526x^81+4195x^82+3202x^83+2646x^84+1726x^85+1332x^86+712x^87+355x^88+272x^89+163x^90+58x^91+24x^92+32x^93+14x^94+2x^96+6x^97+3x^98+4x^99+2x^100

The gray image is a linear code over GF(2) with n=312, k=16 and d=134.
This code was found by Heurico 1.13 in 63.9 seconds.