The generator matrix

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

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+64x^44+298x^45+86x^46+408x^47+121x^48+300x^49+112x^50+252x^51+48x^52+140x^53+48x^54+96x^55+22x^56+28x^57+8x^58+12x^59+2x^61+2x^62

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 0.16 seconds.