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

generates a code of length 54 over Z4 who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+18x^39+148x^40+286x^41+487x^42+740x^43+891x^44+1236x^45+1651x^46+2042x^47+2400x^48+3046x^49+3702x^50+4054x^51+4543x^52+4804x^53+4982x^54+4940x^55+4581x^56+4318x^57+3865x^58+3122x^59+2532x^60+2088x^61+1507x^62+1166x^63+893x^64+518x^65+392x^66+270x^67+127x^68+80x^69+52x^70+26x^71+9x^72+8x^73+2x^74+6x^75+3x^76

The gray image is a code over GF(2) with n=108, k=16 and d=39.
This code was found by Heurico 1.10 in 380 seconds.