The generator matrix

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

generates a code of length 69 over Z4 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+47x^54+12x^55+153x^56+130x^57+279x^58+256x^59+406x^60+382x^61+584x^62+662x^63+800x^64+962x^65+869x^66+1122x^67+968x^68+1146x^69+988x^70+1096x^71+873x^72+950x^73+805x^74+708x^75+564x^76+418x^77+372x^78+214x^79+239x^80+102x^81+123x^82+26x^83+75x^84+6x^85+25x^86+14x^88+4x^90+2x^92+1x^116

The gray image is a code over GF(2) with n=138, k=14 and d=54.
This code was found by Heurico 1.16 in 47.3 seconds.