The generator matrix

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

generates a code of length 10 over F4[X]/(X^2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+192x^21+1248x^22+1086x^24+1728x^25+3744x^26+3072x^27+6096x^28+5184x^29+13344x^30+9216x^31+9135x^32+5184x^33+6240x^34+48x^36+18x^40

The gray image is a linear code over GF(4) with n=40, k=8 and d=21.
This code was found by Heurico 1.16 in 1.05 seconds.