The generator matrix

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

generates a code of length 51 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 149.

Homogenous weight enumerator: w(x)=1x^0+120x^149+288x^150+33x^152+192x^153+192x^154+24x^156+48x^157+72x^158+3x^160+24x^165+24x^166+3x^184

The gray image is a linear code over GF(4) with n=204, k=5 and d=149.
This code was found by Heurico 1.16 in 0.625 seconds.