The generator matrix

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

generates a code of length 54 over F4[X]/(X^2) who´s minimum homogenous weight is 152.

Homogenous weight enumerator: w(x)=1x^0+1539x^152+3480x^156+3600x^160+3024x^164+2874x^168+1464x^172+396x^176+3x^184+3x^192

The gray image is a linear code over GF(4) with n=216, k=7 and d=152.
This code was found by Heurico 1.16 in 11.5 seconds.