The generator matrix
1 0 1 1 1 1 1 1 1 1 1 1 1 X X 0
0 1 1 a a^2*X+a^2 0 a^2*X+1 a^2*X+a^2 X a a*X+1 a^2*X+a a^2 X 1 1
0 0 a^2*X a*X X X 0 a^2*X a*X a^2*X a*X X 0 X 0 a*X
generates a code of length 16 over F4[X]/(X^2) who´s minimum homogenous weight is 44.
Homogenous weight enumerator: w(x)=1x^0+369x^44+279x^48+372x^52+3x^60
The gray image is a linear code over GF(4) with n=64, k=5 and d=44.
This code was found by Heurico 1.16 in -1.01e-007 seconds.