The generator matrix

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

generates a code of length 50 over F4[X]/(X^2) who´s minimum homogenous weight is 136.

Homogenous weight enumerator: w(x)=1x^0+306x^136+24x^137+156x^139+990x^140+228x^141+456x^143+1377x^144+480x^145+552x^147+2229x^148+984x^149+960x^151+2538x^152+936x^153+732x^155+1992x^156+420x^157+216x^159+576x^160+123x^164+39x^168+27x^172+18x^176+12x^180+9x^184+3x^188

The gray image is a linear code over GF(4) with n=200, k=7 and d=136.
This code was found by Heurico 1.16 in 1.07 seconds.