The generator matrix

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

generates a code of length 54 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 148.

Homogenous weight enumerator: w(x)=1x^0+315x^148+144x^149+180x^151+930x^152+396x^153+408x^155+1509x^156+504x^157+552x^159+2121x^160+564x^161+1008x^163+2661x^164+672x^165+708x^167+1824x^168+564x^169+216x^171+690x^172+216x^173+81x^176+12x^177+18x^180+24x^184+27x^188+15x^192+12x^196+12x^200

The gray image is a linear code over GF(4) with n=216, k=7 and d=148.
This code was found by Heurico 1.16 in 1.19 seconds.