The generator matrix

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

generates a code of length 8 over F4[X]/(X^2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+120x^18+216x^19+18x^20+96x^21+720x^22+432x^23+606x^24+288x^25+1080x^26+504x^27+6x^28+9x^32

The gray image is a linear code over GF(4) with n=32, k=6 and d=18.
This code was found by Heurico 1.16 in 0.016 seconds.