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

generates a code of length 93 over Z2[X]/(X^3) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+160x^84+16x^85+278x^86+64x^87+345x^88+136x^89+380x^90+200x^91+485x^92+208x^93+446x^94+176x^95+344x^96+136x^97+214x^98+72x^99+148x^100+16x^101+82x^102+81x^104+52x^106+30x^108+18x^110+5x^112+2x^114+1x^140

The gray image is a linear code over GF(2) with n=372, k=12 and d=168.
This code was found by Heurico 1.16 in 2.57 seconds.