The generator matrix

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

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+456x^136+924x^137+912x^138+540x^139+1731x^140+2520x^141+1980x^142+1212x^143+2832x^144+3720x^145+2724x^146+1476x^147+4296x^148+5076x^149+3432x^150+1968x^151+4851x^152+5796x^153+3696x^154+1500x^155+3567x^156+3672x^157+2148x^158+852x^159+1482x^160+1176x^161+444x^162+132x^163+222x^164+156x^165+24x^166+9x^168+9x^176

The gray image is a linear code over GF(4) with n=200, k=8 and d=136.
This code was found by Heurico 1.16 in 15.7 seconds.