The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  X  1  1  1 X^2  1  1  1 X^2+X  1 X^2+X  1  1  X  1  1  1  1  1  1 X^2+X  1  0  1  1  1  1  0  1  0  X  1 X^2  X  1  X X^2+X  1  1  0
 0  1  1 X^2+X X^2+X+1  1  0 X+1  1  X  1 X^2+1 X^2 X^2+X+1  1  0 X^2+X X^2+1  1 X^2+1  1 X^2+X X+1  1 X+1 X^2+X  X X^2+1 X+1 X^2+1  1  0  1  0 X^2+X+1  1 X^2+X  1 X^2+X+1  1 X^2  X  1  1  X  1  1  X X^2+X+1 X^2
 0  0  X  0 X^2+X  0 X^2+X X^2  X  X  X X^2 X^2+X  X  X X^2 X^2+X X^2 X^2  X X^2+X  0  0  X  0  0 X^2+X X^2 X^2+X  X  0  0  0 X^2 X^2+X X^2+X X^2+X  0  0 X^2+X X^2+X X^2 X^2+X X^2  0  0 X^2  X  X  0
 0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2  0
 0  0  0  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2
 0  0  0  0  0 X^2  0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0
 0  0  0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2 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+369x^44+460x^46+834x^48+840x^50+828x^52+432x^54+220x^56+56x^58+41x^60+4x^62+9x^64+2x^68

The gray image is a linear code over GF(2) with n=200, k=12 and d=88.
This code was found by Heurico 1.16 in 46.2 seconds.