The generator matrix

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

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+35x^44+42x^45+54x^46+80x^47+115x^48+150x^49+126x^50+138x^51+100x^52+54x^53+35x^54+30x^55+30x^56+10x^57+6x^58+6x^59+5x^60+2x^62+2x^63+2x^64+1x^86

The gray image is a linear code over GF(2) with n=200, k=10 and d=88.
This code was found by Heurico 1.16 in 0.112 seconds.