The generator matrix

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

generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+79x^70+154x^71+226x^72+150x^73+108x^74+38x^75+58x^76+26x^77+27x^78+44x^79+41x^80+32x^81+24x^82+4x^87+8x^88+2x^90+2x^92

The gray image is a linear code over GF(2) with n=296, k=10 and d=140.
This code was found by Heurico 1.11 in 0.172 seconds.