The generator matrix

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

generates a code of length 8 over F4[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+714x^16+2688x^18+2016x^20+16128x^22+16392x^24+24192x^26+3360x^28+45x^32

The gray image is a linear code over GF(4) with n=32, k=8 and d=16.
This code was found by Heurico 1.16 in 0.703 seconds.