The generator matrix

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

generates a code of length 29 over Z4 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+20x^26+32x^27+14x^28+16x^29+7x^30+8x^31+15x^32+4x^34+8x^35+2x^36+1x^46

The gray image is a code over GF(2) with n=58, k=7 and d=26.
This code was found by Heurico 1.10 in 0 seconds.