The generator matrix

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

generates a code of length 73 over Z4 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+111x^56+516x^58+1232x^60+1974x^62+3300x^64+4416x^66+5701x^68+7056x^70+8126x^72+8294x^74+7521x^76+6102x^78+4675x^80+3012x^82+1788x^84+908x^86+445x^88+210x^90+109x^92+24x^94+14x^96+1x^100

The gray image is a code over GF(2) with n=146, k=16 and d=56.
This code was found by Heurico 1.10 in 541 seconds.