The generator matrix

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

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+72x^21+480x^22+222x^24+648x^25+1440x^26+384x^27+912x^28+1944x^29+3360x^30+1152x^31+1359x^32+1944x^33+2400x^34+48x^36+18x^40

The gray image is a linear code over GF(4) with n=40, k=7 and d=21.
This code was found by Heurico 1.16 in 0.0819 seconds.