The generator matrix

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

generates a code of length 8 over F4[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+21x^12+105x^16+210x^20+3366x^24+297x^28+96x^32

The gray image is a linear code over GF(4) with n=32, k=6 and d=12.
This code was found by Heurico 1.16 in 0.00435 seconds.