The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+1260x^156+1224x^160+564x^164+492x^168+432x^172+120x^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 3.75 seconds.