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  1  1  1  1  1  1  1  1  1  1  1  X  0  1  1  X  1  X  1  1  1  1  X  1  X
 0  X  0  X  0  0  X X^2+X X^2 X^2  X X^2+X X^2+X X^2+X X^2 X^2  0  X X^2  X  X X^2  0  X X^2+X  X  0  0  0  0  X X^2+X  0  0 X^2 X^2  0  0  X  X  0 X^2 X^2 X^2+X X^2+X X^2+X X^2 X^2+X X^2  0
 0  0  X  X  0 X^2+X  X X^2  0  X  X  0 X^2  X X^2 X^2+X  0 X^2+X X^2+X X^2 X^2 X^2+X  0 X^2+X  0  0  0 X^2  X  X  X  X  0 X^2  X X^2+X X^2+X  X  X X^2+X X^2+X  0  X X^2+X X^2+X X^2+X  0 X^2 X^2+X X^2
 0  0  0 X^2  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0  0  0  0  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2
 0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2  0  0 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+55x^44+98x^46+16x^47+172x^48+112x^49+160x^50+112x^51+137x^52+16x^53+74x^54+40x^56+20x^58+8x^60+2x^64+1x^88

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 0.114 seconds.