The generator matrix
1 1 1 1 1 1 1 1 1 1 X X 1 1 1 1 X 1 1
0 X 0 0 0 0 0 X X a*X X X 0 X 0 X X 0 X
0 0 X 0 0 0 X a^2*X a^2*X 0 a*X a*X 0 X a^2*X X a*X a^2*X a^2*X
0 0 0 X 0 0 a^2*X X 0 a*X a^2*X a*X a*X 0 a^2*X a*X X 0 0
0 0 0 0 X 0 X a^2*X a*X a^2*X 0 X X a^2*X X 0 a*X a^2*X 0
0 0 0 0 0 X a^2*X X a^2*X a^2*X a*X a^2*X X a^2*X a*X a^2*X a*X X X
generates a code of length 19 over F4[X]/(X^2) who´s minimum homogenous weight is 40.
Homogenous weight enumerator: w(x)=1x^0+60x^40+345x^44+615x^48+2247x^52+5871x^56+6165x^60+708x^64+237x^68+105x^72+30x^76
The gray image is a linear code over GF(4) with n=76, k=7 and d=40.
This code was found by Heurico 1.16 in 0.503 seconds.