The generator matrix

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

generates a code of length 28 over Z4 who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+116x^18+222x^19+441x^20+638x^21+1023x^22+1436x^23+1881x^24+2508x^25+2922x^26+3336x^27+3495x^28+3408x^29+3082x^30+2564x^31+1945x^32+1484x^33+948x^34+602x^35+403x^36+146x^37+95x^38+32x^39+21x^40+8x^41+6x^42+5x^44

The gray image is a code over GF(2) with n=56, k=15 and d=18.
This code was found by Heurico 1.16 in 33 seconds.