The generator matrix

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

generates a code of length 51 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 146.

Homogenous weight enumerator: w(x)=1x^0+432x^146+468x^147+90x^148+780x^150+444x^151+75x^152+492x^154+252x^155+24x^156+264x^158+180x^159+48x^160+204x^162+144x^163+6x^164+132x^166+48x^167+9x^168+3x^176

The gray image is a linear code over GF(4) with n=204, k=6 and d=146.
This code was found by Heurico 1.16 in 0.063 seconds.