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

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+393x^136+1008x^137+648x^138+612x^139+1488x^140+3276x^141+1572x^142+1284x^143+2649x^144+4416x^145+2352x^146+1944x^147+3249x^148+6120x^149+2724x^150+2436x^151+3993x^152+6660x^153+2892x^154+1968x^155+3054x^156+4368x^157+1776x^158+840x^159+1326x^160+1692x^161+300x^162+132x^163+216x^164+108x^165+24x^166+6x^168+6x^172+3x^180

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 23.3 seconds.