The generator matrix

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

generates a code of length 51 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 139.

Homogenous weight enumerator: w(x)=1x^0+1020x^139+636x^140+4704x^143+1782x^144+7356x^147+2955x^148+10176x^151+3432x^152+12276x^155+3852x^156+9216x^159+2553x^160+3924x^163+1098x^164+480x^167+72x^168+3x^180

The gray image is a linear code over GF(4) with n=204, k=8 and d=139.
This code was found by Heurico 1.16 in 14.1 seconds.