The generator matrix

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

generates a code of length 10 over F4[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+9x^24+27x^28+192x^30+12x^32+9x^36+6x^40

The gray image is a linear code over GF(4) with n=40, k=4 and d=24.
This code was found by Heurico 1.16 in 1.01e-007 seconds.