The generator matrix

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

generates a code of length 10 over F4[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+90x^20+48x^21+756x^24+432x^25+768x^27+3636x^28+1296x^29+2304x^31+5499x^32+1296x^33+210x^36+48x^40

The gray image is a linear code over GF(4) with n=40, k=7 and d=20.
This code was found by Heurico 1.16 in 0.0886 seconds.