The generator matrix

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

generates a code of length 51 over F4[X]/(X^2) who´s minimum homogenous weight is 135.

Homogenous weight enumerator: w(x)=1x^0+360x^135+948x^136+648x^137+1044x^138+2604x^139+3072x^140+1596x^141+3636x^142+6768x^143+7716x^144+3840x^145+6600x^146+12312x^147+13143x^148+6636x^149+11148x^150+18336x^151+20073x^152+9468x^153+14532x^154+21900x^155+20997x^156+8964x^157+12012x^158+16032x^159+13227x^160+4488x^161+5376x^162+6672x^163+4188x^164+1140x^165+948x^166+1032x^167+504x^168+84x^169+48x^172+24x^176+21x^180+3x^184+3x^188

The gray image is a linear code over GF(4) with n=204, k=9 and d=135.
This code was found by Heurico 1.16 in 181 seconds.