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  1  1  0  1  1  1  0  1  1  1  X  1  1  1  0  1  X  1  1
 0  X  0  X  0  0  X X^2+X X^2 X^2  X X^2+X  0 X^2  X  X  0  X X^2 X^2+X X^2+X  0  X  0 X^2 X^2 X^2+X  X  0  0 X^2+X  X  0 X^2  X X^2+X  0  X X^2  X X^2  0  0  X X^2 X^2+X  X  0 X^2+X  X X^2+X X^2+X  0  X  X X^2+X X^2  X X^2+X  X X^2+X  X X^2  X X^2+X X^2+X  X X^2+X  0  X X^2+X  0 X^2  0
 0  0  X  X  0 X^2+X  X X^2  0  X  X  0  0  X X^2+X  0 X^2  X X^2+X X^2  X  0 X^2 X^2+X X^2  X  0 X^2+X  0 X^2+X  X X^2  0  X  X  0  X X^2+X  0 X^2 X^2+X X^2 X^2+X X^2+X X^2 X^2  0  0 X^2+X  X  0  X X^2  0  X  X X^2 X^2  0  0 X^2+X X^2 X^2 X^2+X X^2+X  0 X^2+X X^2+X X^2  0  X X^2+X  X  0
 0  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2
 0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  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+47x^68+52x^69+64x^70+72x^71+92x^72+140x^73+120x^74+136x^75+88x^76+60x^77+52x^78+40x^79+27x^80+4x^81+14x^82+8x^83+1x^84+4x^86+1x^90+1x^138

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 0.343 seconds.