The generator matrix

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

generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+118x^72+118x^73+173x^74+160x^75+119x^76+74x^77+65x^78+46x^79+28x^80+36x^81+24x^82+2x^83+12x^84+12x^85+24x^86+8x^88+1x^90+1x^92+1x^96+1x^102

The gray image is a linear code over GF(2) with n=304, k=10 and d=144.
This code was found by Heurico 1.16 in 0.26 seconds.