The generator matrix

 1  0  0  0  1  1  1  1 X^2+X  1  1  1 X^2+X  X X^2 X^2+X  X  1 X^2  1  X  1  1  1  1 X^2 X^2  1 X^2  1  1 X^2  1  1 X^2+X  1  1 X^2+X  0 X^2  0  1  1  1  X  1 X^2  1  1 X^2+X X^2+X  1  X  0  1  1  1  1  1  1  1  1  1 X^2  X  1 X^2+X X^2  X  1 X^2+X X^2 X^2  0  1  0
 0  1  0  0  0 X^2  1 X^2+1  1 X^2 X^2+X+1 X+1  1  1  0  1 X^2  1  1 X^2  X  1 X^2 X^2+X X^2+1  1  1  X  X X^2+1 X^2+1  X X^2+X+1 X^2 X^2+X X^2+X  X  1  1  1  1 X+1 X^2+X+1 X^2 X^2 X+1  1 X^2+X X^2+1  1  X  0  1 X^2 X^2+1  X  0 X^2+X  1 X^2+X X^2+X X^2+X+1  X  1  1 X^2+X+1  1  1  1 X^2+X+1 X^2  0 X^2 X^2+X X+1 X^2
 0  0  1  0  0 X^2+1 X^2  1  1 X+1 X^2+X+1 X^2 X+1  X  1  1  1  0 X^2+X+1  X  1 X^2+X+1 X^2+1  1 X^2+X  X  0 X^2  1 X^2+X+1 X^2+X X^2+X X^2+X+1  X  1  X X^2+1  1  1  0  1  0 X^2+X X^2+1 X^2 X^2+X X^2 X^2 X^2+X+1 X^2+X+1  1 X^2 X^2+X+1  1 X+1 X^2+X+1  1 X^2 X^2 X^2+1  1 X^2+X+1 X^2+X  0 X+1  X  X X^2+X  X  X  0  1  1  1 X^2  1
 0  0  0  1  1  1 X^2+1  X  1  0 X+1  0  X  1 X+1 X^2+X X^2+X+1 X^2 X+1 X^2  0  X X^2+X+1  X  1 X^2+X+1 X^2+X  1  1 X^2+1 X+1  1 X^2+X+1 X^2+X X^2 X^2+1  1 X^2+X+1 X^2 X+1  1  X X^2 X^2+X  1 X^2+X+1  X X^2+X+1  0 X^2  X X^2+1  0 X^2+1  0  X X^2 X^2  1  1 X^2+X+1  0  0 X+1  0 X^2+1 X^2  1  1 X^2+X  1 X^2+X X^2+X+1 X^2  1 X^2+1
 0  0  0  0  X  0  0  0  0  X  X  X  X  X  X  X  X X^2+X X^2 X^2  0  0 X^2+X X^2 X^2+X X^2 X^2+X  0  0  X  X  X X^2  X  X X^2+X X^2  0  0  X  X X^2+X X^2 X^2 X^2  0  0 X^2 X^2+X  0 X^2 X^2+X  X X^2  0 X^2  X  X X^2  0 X^2+X  0 X^2  0 X^2  X  0 X^2+X X^2+X X^2+X  X X^2  0  0  X  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+589x^68+1524x^70+2405x^72+2534x^74+2774x^76+2364x^78+2031x^80+1230x^82+607x^84+216x^86+97x^88+2x^90+6x^92+2x^96+2x^98

The gray image is a linear code over GF(2) with n=304, k=14 and d=136.
This code was found by Heurico 1.13 in 188 seconds.