The generator matrix

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

generates a code of length 28 over Z4 who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+36x^22+80x^23+90x^24+94x^25+93x^26+100x^27+81x^28+80x^29+93x^30+82x^31+72x^32+46x^33+31x^34+24x^35+11x^36+4x^37+3x^38+2x^39+1x^40

The gray image is a code over GF(2) with n=56, k=10 and d=22.
This code was found by Heurico 1.16 in 0.0448 seconds.