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.