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

generates a code of length 38 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 100.

Homogenous weight enumerator: w(x)=1x^0+72x^100+183x^104+177x^108+768x^111+162x^112+2304x^115+84x^116+117x^120+87x^124+54x^128+45x^132+24x^136+12x^140+3x^144+3x^148

The gray image is a linear code over GF(4) with n=152, k=6 and d=100.
This code was found by Heurico 1.16 in 0.104 seconds.