The generator matrix

 1  1  1  1  1  1
 0  X  0  0  X  X
 0  0  X  0 5X 4X
 0  0  0  X 5X  X

generates a code of length 6 over Z7[X]/(X^2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+120x^21+360x^28+972x^35+14406x^36+948x^42

The gray image is a linear code over GF(7) with n=42, k=5 and d=21.
This code was found by Heurico 1.16 in 0.00595 seconds.