The generator matrix

 1  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  X  0 a*X a*X  X
 0  0  X  0  0 a^2*X  X  0 a*X a*X
 0  0  0  X  0  X a^2*X a^2*X a*X  0
 0  0  0  0  X a^2*X a*X  X a^2*X  X

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

Homogenous weight enumerator: w(x)=1x^0+90x^20+180x^24+180x^28+3072x^30+315x^32+210x^36+48x^40

The gray image is a linear code over GF(4) with n=40, k=6 and d=20.
This code was found by Heurico 1.16 in 0.0109 seconds.