The generator matrix

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

generates a code of length 54 over F4[X]/(X^2) who´s minimum homogenous weight is 148.

Homogenous weight enumerator: w(x)=1x^0+105x^148+204x^152+345x^156+1311x^160+1821x^164+78x^168+48x^172+45x^176+51x^180+42x^184+27x^188+12x^192+3x^196+3x^208

The gray image is a linear code over GF(4) with n=216, k=6 and d=148.
This code was found by Heurico 1.16 in 0.169 seconds.