The generator matrix

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

generates a code of length 54 over F4[X]/(X^2) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+672x^144+900x^145+828x^146+864x^147+2691x^148+3684x^149+2952x^150+2316x^151+6600x^152+7884x^153+5988x^154+4632x^155+11922x^156+13716x^157+9816x^158+7152x^159+17898x^160+19632x^161+13416x^162+9312x^163+20298x^164+20556x^165+12984x^166+8460x^167+15759x^168+14364x^169+7140x^170+3288x^171+6705x^172+4764x^173+1992x^174+792x^175+1278x^176+516x^177+180x^178+48x^179+75x^180+33x^184+15x^188+9x^192+6x^196+6x^200

The gray image is a linear code over GF(4) with n=216, k=9 and d=144.
This code was found by Heurico 1.16 in 207 seconds.