The generator matrix

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

generates a code of length 53 over Z4 who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+32x^39+90x^40+204x^41+339x^42+486x^43+685x^44+890x^45+1110x^46+1268x^47+1539x^48+1734x^49+2053x^50+2156x^51+2399x^52+2542x^53+2324x^54+2460x^55+2050x^56+1884x^57+1652x^58+1290x^59+1133x^60+778x^61+574x^62+424x^63+262x^64+146x^65+121x^66+68x^67+29x^68+14x^69+16x^70+8x^71+2x^72+3x^74+2x^76

The gray image is a code over GF(2) with n=106, k=15 and d=39.
This code was found by Heurico 1.16 in 99.1 seconds.