The generator matrix

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

generates a code of length 54 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 152.

Homogenous weight enumerator: w(x)=1x^0+1623x^152+3120x^156+3912x^160+3264x^164+2622x^168+1296x^172+540x^176+3x^184+3x^192

The gray image is a linear code over GF(4) with n=216, k=7 and d=152.
This code was found by Heurico 1.16 in 486 seconds.