The generator matrix

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

generates a code of length 10 over F4[X]/(X^2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+228x^18+360x^19+90x^20+768x^21+2736x^22+1440x^23+3828x^24+6912x^25+12312x^26+18864x^27+22068x^28+20736x^29+46128x^30+48672x^31+33147x^32+20736x^33+18468x^34+4392x^35+210x^36+48x^40

The gray image is a linear code over GF(4) with n=40, k=9 and d=18.
This code was found by Heurico 1.16 in 13 seconds.