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

generates a code of length 71 over Z4 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+94x^54+437x^56+1212x^58+2057x^60+2986x^62+4440x^64+5888x^66+7317x^68+8006x^70+8363x^72+7572x^74+6208x^76+4592x^78+2980x^80+1682x^82+1025x^84+408x^86+158x^88+60x^90+33x^92+10x^94+5x^96+2x^98

The gray image is a code over GF(2) with n=142, k=16 and d=54.
This code was found by Heurico 1.10 in 239 seconds.