The generator matrix

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

generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+251x^84+132x^85+351x^86+136x^87+307x^88+98x^89+215x^90+44x^91+152x^92+30x^93+83x^94+32x^95+95x^96+18x^97+31x^98+12x^99+16x^100+6x^101+18x^102+8x^104+4x^105+6x^106+1x^108+1x^112

The gray image is a linear code over GF(2) with n=356, k=11 and d=168.
This code was found by Heurico 1.16 in 0.625 seconds.