The generator matrix

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

generates a code of length 23 over Z4 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+27x^14+82x^15+167x^16+250x^17+397x^18+460x^19+571x^20+760x^21+840x^22+976x^23+918x^24+780x^25+650x^26+468x^27+354x^28+248x^29+123x^30+62x^31+34x^32+10x^33+9x^34+3x^36+2x^38

The gray image is a code over GF(2) with n=46, k=13 and d=14.
This code was found by Heurico 1.10 in 0.637 seconds.