The generator matrix

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

generates a code of length 54 over F4[X]/(X^2) who´s minimum homogenous weight is 156.

Homogenous weight enumerator: w(x)=1x^0+1236x^156+1260x^160+576x^164+480x^168+396x^172+144x^176+3x^192

The gray image is a linear code over GF(4) with n=216, k=6 and d=156.
This code was found by Heurico 1.16 in 4.97 seconds.