The generator matrix

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

generates a code of length 23 over Z4 who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+32x^13+86x^14+190x^15+316x^16+446x^17+640x^18+922x^19+1262x^20+1516x^21+1775x^22+1906x^23+1722x^24+1548x^25+1347x^26+1014x^27+733x^28+460x^29+239x^30+128x^31+60x^32+30x^33+9x^34+1x^36+1x^40

The gray image is a code over GF(2) with n=46, k=14 and d=13.
This code was found by Heurico 1.10 in 2.15 seconds.