The generator matrix

 1  0  0  1  1  1  1  1 5X  1  1
 0  1  0 5X+1  3 5X+2 5X 5X+3  1  6  1
 0  0  1 5X+5  3 5X+6 5X+1 5X+4 5X+2 X+3 X+4

generates a code of length 11 over Z7[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+924x^54+1386x^55+66x^56+3234x^60+11088x^61+6930x^62+132x^63+26754x^66+19404x^67+33264x^68+14322x^69+66x^70+78x^77

The gray image is a linear code over GF(7) with n=77, k=6 and d=54.
This code was found by Heurico 1.16 in 0.452 seconds.