The generator matrix

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

generates a code of length 10 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+90x^16+48x^18+252x^20+576x^22+2076x^24+2592x^26+6144x^27+10296x^28+5184x^30+18432x^31+14949x^32+3888x^34+780x^36+228x^40

The gray image is a linear code over GF(4) with n=40, k=8 and d=16.
This code was found by Heurico 1.16 in 0.729 seconds.