The generator matrix

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

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+48x^18+282x^20+576x^22+2061x^24+2592x^26+6144x^27+10236x^28+5184x^30+18432x^31+15054x^32+3888x^34+714x^36+243x^40

The gray image is a linear code over GF(4) with n=40, k=8 and d=16.
This code was found by Heurico 1.16 in 0.732 seconds.