The generator matrix

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

generates a code of length 50 over Z2[X]/(X^3) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+33x^44+112x^45+146x^46+278x^47+167x^48+300x^49+136x^50+246x^51+129x^52+198x^53+78x^54+108x^55+49x^56+24x^57+14x^58+6x^59+2x^60+6x^61+8x^62+2x^63+3x^64+2x^66

The gray image is a linear code over GF(2) with n=200, k=11 and d=88.
This code was found by Heurico 1.16 in 0.211 seconds.