The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+34x^39+77x^40+138x^41+249x^42+352x^43+545x^44+716x^45+932x^46+1022x^47+1279x^48+1596x^49+1748x^50+1994x^51+2120x^52+2226x^53+2350x^54+2438x^55+2235x^56+2084x^57+1817x^58+1580x^59+1378x^60+1064x^61+857x^62+602x^63+460x^64+324x^65+198x^66+154x^67+84x^68+42x^69+36x^70+16x^71+12x^72+2x^73+4x^74+1x^76+1x^78

The gray image is a code over GF(2) with n=108, k=15 and d=39.
This code was found by Heurico 1.16 in 99.8 seconds.