The generator matrix

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

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+153x^12+120x^13+768x^15+1689x^16+480x^17+4224x^18+6912x^19+7338x^20+18576x^21+25344x^22+20736x^23+51414x^24+53088x^25+38016x^26+20736x^27+10989x^28+1464x^29+96x^32

The gray image is a linear code over GF(4) with n=32, k=9 and d=12.
This code was found by Heurico 1.16 in 6.73 seconds.