The generator matrix

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

generates a code of length 51 over F4[X]/(X^2) who´s minimum homogenous weight is 146.

Homogenous weight enumerator: w(x)=1x^0+396x^146+504x^147+90x^148+816x^150+408x^151+72x^152+504x^154+264x^155+24x^156+252x^158+144x^159+51x^160+228x^162+144x^163+6x^164+108x^166+72x^167+12x^168

The gray image is a linear code over GF(4) with n=204, k=6 and d=146.
This code was found by Heurico 1.16 in 0.063 seconds.