The generator matrix

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

generates a code of length 51 over F4[X]/(X^2) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+243x^144+348x^146+726x^148+348x^150+585x^152+324x^154+462x^156+372x^158+276x^160+144x^162+222x^164+30x^168+6x^172+6x^176+3x^184

The gray image is a linear code over GF(4) with n=204, k=6 and d=144.
This code was found by Heurico 1.16 in 0.0823 seconds.