The generator matrix

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

generates a code of length 69 over Z4 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+101x^52+16x^54+386x^56+198x^58+929x^60+732x^62+1898x^64+1612x^66+2437x^68+1910x^70+2230x^72+1230x^74+1450x^76+376x^78+556x^80+64x^82+186x^84+6x^86+48x^88+16x^92+1x^96+1x^108

The gray image is a code over GF(2) with n=138, k=14 and d=52.
This code was found by Heurico 1.16 in 49.2 seconds.