The generator matrix

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

generates a code of length 51 over F4[X]/(X^2) who´s minimum homogenous weight is 147.

Homogenous weight enumerator: w(x)=1x^0+972x^147+417x^148+828x^151+216x^152+516x^155+192x^156+372x^159+87x^160+288x^163+108x^164+96x^167+3x^180

The gray image is a linear code over GF(4) with n=204, k=6 and d=147.
This code was found by Heurico 1.16 in 95.8 seconds.