The generator matrix

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

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+30x^8+192x^9+267x^12+1152x^13+1152x^15+741x^16+2304x^17+3072x^18+6912x^19+846x^20+21888x^21+9216x^22+10368x^23+2028x^24+5184x^25+183x^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 0.291 seconds.