The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+45x^8+138x^12+405x^16+780x^20+13371x^24+1098x^28+546x^32

The gray image is a linear code over GF(4) with n=32, k=7 and d=8.
This code was found by Heurico 1.16 in 0.0438 seconds.