The generator matrix

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

generates a code of length 50 over F4[X]/(X^2) who´s minimum homogenous weight is 134.

Homogenous weight enumerator: w(x)=1x^0+96x^134+444x^135+519x^136+480x^137+696x^138+1356x^139+1203x^140+1656x^141+1824x^142+2784x^143+1989x^144+2364x^145+2580x^146+4128x^147+2646x^148+3552x^149+4080x^150+5532x^151+3144x^152+4200x^153+3792x^154+4812x^155+2466x^156+2568x^157+1968x^158+1992x^159+1074x^160+540x^161+324x^162+456x^163+171x^164+24x^168+24x^172+24x^176+15x^180+9x^184+3x^188

The gray image is a linear code over GF(4) with n=200, k=8 and d=134.
This code was found by Heurico 1.16 in 14 seconds.