The generator matrix

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

generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+324x^68+782x^70+835x^72+670x^74+552x^76+400x^78+258x^80+142x^82+97x^84+22x^86+10x^88+3x^92

The gray image is a linear code over GF(2) with n=296, k=12 and d=136.
This code was found by Heurico 1.16 in 16.3 seconds.