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  1  1  1  1  1  1  1 X^2 X^2+X  1 X^2+X  X  X  1  1  1  1  1  1  X  1  1  1  1  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 X+1 X^2+X+1  X X^2+X X^2+X+1 X^2+X X+1 X^2  X  X X^2+X  0  0 X^2+X X^2+X X^2+X X^2+X X+1 X^2+X+1 X^2+X X^2+1 X^2+1  X  X X+1  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^2+1  1 X^2  X X^2+X X^2+X+1  1  1 X+1  1  1  1 X+1  0 X^2  1  X X^2+X+1  1 X+1 X^2 X^2  1 X^2+X+1 X+1
 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  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2 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+126x^72+106x^73+239x^74+120x^75+81x^76+64x^77+63x^78+60x^79+22x^80+22x^81+57x^82+12x^83+28x^84+6x^86+13x^88+2x^90+1x^92+1x^94

The gray image is a linear code over GF(2) with n=304, k=10 and d=144.
This code was found by Heurico 1.11 in 0.188 seconds.