The generator matrix

1 0 0 0 0 1 1 1 1 2 1 2 1 1 1 0 1 0 0 2 1 2 1 1 1 2 2 2 1 1 2 2 1 2 0 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 2
0 1 0 0 0 0 0 0 2 0 0 2 2 1 3 1 1 1 1 1 1 2 3 0 3 1 0 1 2 3 2 1 3 0 1 3 1 2 2 0 2 0 1 1 0 1 2 1 0 3 2
0 0 1 0 0 0 0 1 1 1 2 1 1 1 0 1 3 2 2 3 0 2 0 1 2 2 0 1 3 1 0 0 1 1 3 2 1 2 1 2 1 0 0 0 1 2 0 1 0 2 0
0 0 0 1 0 1 0 2 1 1 1 1 3 3 1 1 1 3 2 1 2 0 0 0 1 1 1 2 3 1 1 0 0 1 2 1 3 0 0 3 2 2 3 0 2 0 2 0 2 0 0
0 0 0 0 1 1 3 3 1 0 2 3 2 1 2 3 0 0 1 2 0 1 1 2 1 1 3 0 2 0 3 2 2 2 1 1 2 3 0 2 2 0 0 2 0 3 3 0 3 1 0
0 0 0 0 0 2 2 2 2 0 0 2 0 2 0 2 0 0 2 0 0 2 2 0 2 2 2 2 2 2 0 2 2 2 0 0 2 0 2 2 2 2 2 2 2 0 0 0 0 2 0

generates a code of length 51 over Z4 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+302x^44+98x^46+512x^48+110x^50+400x^52+88x^54+300x^56+64x^58+130x^60+22x^62+19x^64+2x^66

The gray image is a code over GF(2) with n=102, k=11 and d=44.
This code was found by Heurico 1.10 in 368 seconds.