The generator matrix

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

generates a code of length 26 over Z4 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+165x^16+136x^17+493x^18+574x^19+1117x^20+1342x^21+1932x^22+2514x^23+2866x^24+3512x^25+3198x^26+3748x^27+2854x^28+2628x^29+2073x^30+1228x^31+1064x^32+560x^33+453x^34+126x^35+125x^36+14x^37+42x^38+2x^39+1x^46

The gray image is a code over GF(2) with n=52, k=15 and d=16.
This code was found by Heurico 1.16 in 26.2 seconds.