The generator matrix

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

generates a code of length 10 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+120x^19+90x^20+192x^21+480x^23+2676x^24+1728x^25+3216x^27+15156x^28+5184x^29+7008x^31+22779x^32+5184x^33+1464x^35+210x^36+48x^40

The gray image is a linear code over GF(4) with n=40, k=8 and d=19.
This code was found by Heurico 1.16 in 66.1 seconds.