The generator matrix

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

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+56x^68+94x^70+8x^71+138x^72+120x^73+236x^74+120x^75+117x^76+8x^77+44x^78+49x^80+20x^82+6x^84+6x^86+1x^140

The gray image is a linear code over GF(2) with n=296, k=10 and d=136.
This code was found by Heurico 1.16 in 0.338 seconds.