The generator matrix

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

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+36x^12+246x^16+840x^20+3072x^21+1632x^24+9216x^25+1236x^28+105x^32

The gray image is a linear code over GF(4) with n=32, k=7 and d=12.
This code was found by Heurico 1.16 in 0.032 seconds.