The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  1  0  1  1  1  1  X  1  1  1  1  X  1  1  X  1  1  1  1  1  1  1 a^2*X  1  1  X  1  1  1  1  1  1  1  1 a^2*X  X  X
 0  1  1  a a^2*X+a^2  0 a^2*X+1  a a^2*X+a^2  1  0  a a^2*X+1 a^2*X+a^2  1  X a^2*X+1 X+a a*X+a^2  1  X  1 X+a a*X+a^2  1  X a*X+1  1 X+a a^2 a^2*X+1 a*X+1 X+1  0  a  1 a*X+a a*X+a^2  1 a^2*X+1  X a^2*X+a^2 a^2*X X+a a*X+a^2 a*X+a a^2*X  1 a*X  1
 0  0 a^2*X  0  X  0  X a*X a*X a*X a*X  X a^2*X a^2*X  0 a^2*X  0 a^2*X  0  X  X a*X a*X  X a^2*X a*X  X a*X a^2*X a*X  0 a^2*X a^2*X a*X a*X  0  X  X a*X  X a^2*X  X  0 a*X a^2*X  0  0  0 a^2*X a^2*X
 0  0  0  X a*X a*X  0 a*X  X  X  0  X a*X  X  X  0  0  X  X  X  0  0  X  X  X a*X a*X  0 a*X a*X a*X a^2*X  X  X  0 a^2*X a^2*X a^2*X a^2*X  X a*X  0 a^2*X a^2*X a^2*X  0  X a*X  X a^2*X

generates a code of length 50 over F4[X]/(X^2) who´s minimum homogenous weight is 141.

Homogenous weight enumerator: w(x)=1x^0+372x^141+369x^144+660x^145+192x^148+780x^149+168x^152+540x^153+186x^156+528x^157+87x^160+192x^161+12x^168+6x^172+3x^176

The gray image is a linear code over GF(4) with n=200, k=6 and d=141.
This code was found by Heurico 1.16 in 42.8 seconds.