The generator matrix

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

generates a code of length 7 over F4[X]/(X^2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+63x^8+48x^9+210x^12+576x^13+735x^16+2592x^17+9216x^18+1260x^20+17472x^21+27648x^22+1281x^24+3888x^25+546x^28

The gray image is a linear code over GF(4) with n=28, k=8 and d=8.
This code was found by Heurico 1.16 in 0.357 seconds.