The generator matrix

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

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+178x^68+336x^69+414x^70+376x^71+440x^72+344x^73+394x^74+316x^75+267x^76+236x^77+164x^78+152x^79+169x^80+84x^81+48x^82+44x^83+69x^84+20x^85+26x^86+8x^87+4x^88+4x^89+2x^90

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 0.821 seconds.