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

generates a code of length 68 over Z4 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+78x^52+163x^54+349x^56+516x^58+861x^60+1299x^62+1733x^64+2146x^66+2137x^68+2099x^70+1776x^72+1290x^74+859x^76+512x^78+282x^80+142x^82+93x^84+22x^86+19x^88+2x^90+4x^92+1x^110

The gray image is a code over GF(2) with n=136, k=14 and d=52.
This code was found by Heurico 1.16 in 49.4 seconds.