The generator matrix

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

generates a code of length 54 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 147.

Homogenous weight enumerator: w(x)=1x^0+300x^147+453x^148+432x^149+984x^150+1452x^151+1902x^152+1404x^153+2064x^154+2832x^155+2994x^156+1704x^157+2748x^158+3960x^159+3813x^160+2280x^161+3408x^162+4440x^163+4791x^164+2148x^165+3324x^166+4344x^167+3636x^168+2064x^169+2076x^170+2124x^171+1620x^172+660x^173+672x^174+468x^175+234x^176+60x^177+84x^178+48x^179+6x^180+6x^184

The gray image is a linear code over GF(4) with n=216, k=8 and d=147.
This code was found by Heurico 1.16 in 13.8 seconds.