The generator matrix

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

generates a code of length 7 over F4[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+234x^12+240x^13+1152x^15+1557x^16+1008x^17+5760x^18+6912x^19+5040x^20+9552x^21+17280x^22+10368x^23+4914x^24+1488x^25+30x^28

The gray image is a linear code over GF(4) with n=28, k=8 and d=12.
This code was found by Heurico 1.16 in 0.468 seconds.