The generator matrix

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

generates a code of length 54 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 146.

Homogenous weight enumerator: w(x)=1x^0+240x^146+468x^147+135x^148+276x^149+1704x^150+2040x^151+171x^152+960x^153+3216x^154+3636x^155+165x^156+1500x^157+4824x^158+5268x^159+108x^160+2208x^161+6504x^162+6876x^163+108x^164+2316x^165+6216x^166+5760x^167+105x^168+1632x^169+3792x^170+2940x^171+60x^172+324x^173+1080x^174+660x^175+54x^176+72x^178+36x^180+36x^184+21x^188+15x^192+3x^196+6x^200

The gray image is a linear code over GF(4) with n=216, k=8 and d=146.
This code was found by Heurico 1.16 in 17.8 seconds.