The generator matrix

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

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+30x^16+144x^18+60x^20+384x^21+864x^22+60x^24+1152x^25+1296x^26+84x^28+21x^32

The gray image is a linear code over GF(4) with n=32, k=6 and d=16.
This code was found by Heurico 1.16 in 0.00424 seconds.