The generator matrix

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

generates a code of length 23 over Z4 who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+88x^12+16x^13+133x^14+176x^15+617x^16+720x^17+1088x^18+1856x^19+2588x^20+3360x^21+3765x^22+4128x^23+3491x^24+3360x^25+2600x^26+1856x^27+1288x^28+720x^29+511x^30+176x^31+114x^32+16x^33+88x^34+4x^36+7x^38+1x^40

The gray image is a code over GF(2) with n=46, k=15 and d=12.
This code was found by Heurico 1.16 in 9.38 seconds.