The generator matrix

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

generates a code of length 54 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 153.

Homogenous weight enumerator: w(x)=1x^0+216x^153+378x^156+924x^157+204x^160+780x^161+132x^164+420x^165+180x^168+492x^169+108x^172+240x^173+12x^176+6x^188+3x^192

The gray image is a linear code over GF(4) with n=216, k=6 and d=153.
This code was found by Heurico 1.16 in 4.33 seconds.