The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1  2  2  2  2  1  1  2  1  1  1  1
 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  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  2  2  2  0  2  2  2  0  0  0  2  2  2  0  2  2  2  2  0  0  0
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0  2  2  2  2  0  2  0  2  0  0  2  0  2  2  2  2  0  0  0  2  0  0  0  2  2  2  2  2  2  0  0  2  0  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  0  0  2  0  0  2  2  0  0  2  0  0  2  0  0  0  2  0  2  2  0  2  2  2  2  2  0  2  0  2  0  2  2  2  0  0  2  2  2  2  2  0
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  0  0  0  0  2  2  0  2  0  0  2  2  2  2  2  2  0  0  2  2  0  0  2  0  0  0  0  2  0  2  2  0  0  2  0  2  2  2  2  2  0  2  2  2  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  2  0  2  2  0  2  2  2  0  0  0  2  2  0  2  2  0  2  0  0  0  0  2  2  0  0  2  0  2  0  2  2  2  0  2  2  0  2  0  2  2  2  2  0  0  0  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  2  2  0  2  2  0  2  0  2  0  2  2  2  0  2  0  2  0  0  2  0  2  2  0  2  2  0  0  2  0  2  2  0  0  0  0  0  0  2  0  0  2  2  0  0  2  0  0  2  0  0  0  0
 0  0  0  0  0  0  0  2  0  0  0  0  0  2  0  0  0  2  2  2  2  0  2  2  0  2  0  2  0  2  0  0  0  0  2  0  0  2  0  2  2  2  0  2  2  0  2  0  2  2  2  0  0  2  0  2  2  2  0  2  2  0  0  0  2  2  2  2  0
 0  0  0  0  0  0  0  0  2  0  0  0  2  0  0  0  0  2  2  0  2  0  0  0  2  2  2  0  0  0  2  2  0  2  2  0  0  2  2  0  2  2  0  2  2  0  0  2  0  2  0  0  2  2  0  0  2  2  2  0  0  0  2  2  0  2  0  0  0
 0  0  0  0  0  0  0  0  0  2  0  0  2  0  0  0  2  0  0  2  0  2  0  0  2  0  0  0  0  2  2  2  0  0  0  2  0  2  2  2  2  0  2  2  2  0  2  0  0  2  2  0  0  0  0  2  0  2  2  0  2  2  0  2  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  0  0  0  2  0  0  2  2  0  0  2  0  2  2  0  2  0  0  2  2  0  0  0  0  2  2  2  0  0  2  2  2  2  2  0  0  0  0  2  2  2  2  2  2  2  2  0  2  0  2  2  0
 0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  0  2  2  2  2  2  0  2  0  2  0  0  0  0  0  2  2  2  0  0  0  2  2  2  0  2  2  2  0  2  2  0  2  2  0  0  2  2  0  2  2  2  2  2  2  2  0  0  0  2  2  0

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

Homogenous weight enumerator: w(x)=1x^0+83x^52+61x^54+234x^56+152x^58+302x^60+238x^62+64x^63+341x^64+384x^65+308x^66+960x^67+332x^68+1280x^69+334x^70+960x^71+310x^72+384x^73+348x^74+64x^75+242x^76+302x^78+130x^80+204x^82+65x^84+85x^86+8x^88+12x^90+3x^94+1x^126

The gray image is a code over GF(2) with n=138, k=13 and d=52.
This code was found by Heurico 1.16 in 17.5 seconds.