The generator matrix

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

generates a code of length 10 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+90x^20+48x^21+756x^24+432x^25+768x^27+3636x^28+1296x^29+2304x^31+5499x^32+1296x^33+210x^36+48x^40

The gray image is a linear code over GF(4) with n=40, k=7 and d=20.
This code was found by Heurico 1.16 in 0.0897 seconds.