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

generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+21x^74+20x^75+44x^76+54x^77+50x^78+126x^79+27x^80+428x^81+24x^82+82x^83+30x^84+12x^85+21x^86+18x^87+12x^88+12x^89+11x^90+10x^91+14x^92+6x^93+1x^150

The gray image is a linear code over GF(2) with n=324, k=10 and d=148.
This code was found by Heurico 1.16 in 0.471 seconds.