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

generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+97x^76+122x^78+32x^79+201x^80+128x^81+220x^82+192x^83+271x^84+128x^85+190x^86+32x^87+164x^88+114x^90+55x^92+48x^94+42x^96+10x^98+1x^148

The gray image is a linear code over GF(2) with n=336, k=11 and d=152.
This code was found by Heurico 1.16 in 0.837 seconds.