The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+81x^16+282x^20+525x^24+1020x^28+12288x^30+1230x^32+714x^36+243x^40

The gray image is a linear code over GF(4) with n=40, k=7 and d=16.
This code was found by Heurico 1.16 in 0.0935 seconds.