The generator matrix

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

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+512x^44+744x^46+993x^48+708x^50+552x^52+368x^54+174x^56+36x^58+8x^60

The gray image is a linear code over GF(2) with n=196, k=12 and d=88.
This code was found by Heurico 1.11 in 50.3 seconds.