The generator matrix

 1  0  0  0  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 aX  1  1  1  1  1  1  X  1  1  1  1  1  1  1  0 (a+1)X  1  1  0  1  1  1  1
 0  1  0  0  0  X  X (a+1)X+1 aX+1  1 aX+a a+1 X+a (a+1)X+a+1  X (a+1)X+1 a+1  1  a  1 (a+1)X  a (a+1)X+a aX+a+1 X+1 X+1 aX X+a (a+1)X+a+1 (a+1)X+1  X (a+1)X+a X+a aX+a+1 (a+1)X X+1 X+1  1 (a+1)X+a+1  0  a (a+1)X+1 (a+1)X (a+1)X (a+1)X+1  1  1 aX+1  0  X a+1 X+a+1 (a+1)X+a X+1
 0  0  1  0  1 (a+1)X+a (a+1)X+a+1  X aX+a aX+a aX  0 aX+a+1 aX+1  a  X aX+1  a a+1 aX aX+a+1  1 X+a  a  1 (a+1)X+1 aX+a aX (a+1)X (a+1)X+1  1 X+1  a aX+1 aX+1 aX+a X+a+1  1 (a+1)X+a (a+1)X+a  0 aX+a+1 aX  1 (a+1)X+a+1 X+a+1 aX+a aX aX+a  1 aX+1 (a+1)X  X X+a
 0  0  0  1 a+1  a  1 (a+1)X+a aX (a+1)X+a (a+1)X+1 X+a+1  a aX+a X+1 aX X+a+1 a+1 X+1 aX+a+1 (a+1)X+a+1 aX  X aX+a a+1  a aX (a+1)X+a (a+1)X+1  X a+1 (a+1)X+a X+1 (a+1)X  X aX+a  a X+a  0 X+a+1 aX+a+1  0 X+1 (a+1)X+1 X+a+1 aX+1 aX (a+1)X+1 aX aX+a (a+1)X+a+1 aX+a+1 (a+1)X  1
 0  0  0  0  X  0 aX  0  0  0 aX  X aX  X (a+1)X aX (a+1)X  0  X  X (a+1)X  0 aX  0 aX (a+1)X aX (a+1)X (a+1)X  X (a+1)X (a+1)X aX  X aX (a+1)X  X (a+1)X (a+1)X aX (a+1)X  0  X  0 aX  0 aX (a+1)X  0 aX  0  0  X aX

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

Homogenous weight enumerator: w(x)=1x^0+597x^144+912x^145+600x^146+1272x^147+2334x^148+4068x^149+2520x^150+3576x^151+5850x^152+8172x^153+4620x^154+6576x^155+10350x^156+14844x^157+7656x^158+11136x^159+14610x^160+20520x^161+10116x^162+14160x^163+17274x^164+23340x^165+10104x^166+11832x^167+13536x^168+14700x^169+5604x^170+5808x^171+5814x^172+5076x^173+1608x^174+912x^175+1191x^176+528x^177+180x^178+24x^179+48x^180+33x^184+27x^188+3x^192+6x^196+3x^200+3x^204

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.