The generator matrix

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

generates a code of length 56 over Z4 who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+40x^39+79x^40+112x^41+166x^42+238x^43+371x^44+478x^45+568x^46+836x^47+968x^48+1120x^49+1342x^50+1476x^51+1651x^52+1768x^53+1970x^54+2060x^55+2094x^56+2140x^57+2006x^58+1780x^59+1732x^60+1586x^61+1372x^62+1124x^63+916x^64+820x^65+564x^66+388x^67+293x^68+248x^69+172x^70+116x^71+75x^72+48x^73+26x^74+6x^75+9x^76+6x^78+3x^80

The gray image is a code over GF(2) with n=112, k=15 and d=39.
This code was found by Heurico 1.16 in 99.9 seconds.