The generator matrix

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

generates a code of length 49 over Z2[X]/(X^3) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+98x^44+152x^45+271x^46+242x^47+290x^48+210x^49+187x^50+142x^51+159x^52+72x^53+77x^54+58x^55+26x^56+14x^57+33x^58+6x^59+9x^60+1x^64

The gray image is a linear code over GF(2) with n=196, k=11 and d=88.
This code was found by Heurico 1.16 in 0.157 seconds.