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.