The generator matrix

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

generates a code of length 50 over F4[X]/(X^2) who´s minimum homogenous weight is 140.

Homogenous weight enumerator: w(x)=1x^0+1491x^140+3189x^144+3744x^148+3528x^152+2730x^156+1407x^160+288x^164+3x^172+3x^176

The gray image is a linear code over GF(4) with n=200, k=7 and d=140.
This code was found by Heurico 1.16 in 66.6 seconds.