The generator matrix

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

generates a code of length 10 over F4[X]/(X^2) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+120x^19+90x^20+192x^21+480x^23+2676x^24+1728x^25+3216x^27+15156x^28+5184x^29+7008x^31+22779x^32+5184x^33+1464x^35+210x^36+48x^40

The gray image is a linear code over GF(4) with n=40, k=8 and d=19.
This code was found by Heurico 1.16 in 70.9 seconds.