The generator matrix

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

generates a code of length 51 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 140.

Homogenous weight enumerator: w(x)=1x^0+144x^140+12x^141+192x^144+144x^145+168x^148+648x^149+162x^152+1296x^153+63x^156+972x^157+75x^160+66x^164+33x^168+57x^172+18x^176+24x^180+15x^184+6x^188

The gray image is a linear code over GF(4) with n=204, k=6 and d=140.
This code was found by Heurico 1.16 in 0.239 seconds.