The generator matrix

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

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+201x^68+286x^69+390x^70+440x^71+465x^72+368x^73+349x^74+312x^75+242x^76+190x^77+197x^78+148x^79+173x^80+92x^81+95x^82+52x^83+38x^84+20x^85+17x^86+8x^87+7x^88+4x^89+1x^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 1.11 in 0.375 seconds.