The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  2  2  2  2  1  1
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  0  0  0  2
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  0  2  0  2
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  2  0  0  2  0  2  0  0
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  0  2  0  2  2  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  2  0  2  2  0  2  0  2  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  0  2  2  0  2  0  0  0  2  0
 0  0  0  0  0  0  0  2  0  0  0  0  0  2  0  2  2  0  2  0  0  0  0
 0  0  0  0  0  0  0  0  2  0  0  0  0  2  0  0  0  2  2  2  0  0  0
 0  0  0  0  0  0  0  0  0  2  0  0  0  2  0  2  2  2  0  2  2  0  0
 0  0  0  0  0  0  0  0  0  0  2  0  0  2  2  2  2  0  0  0  0  2  0
 0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  0  0  0  2  2  2  2  0
 0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  0  0  2  0  0  2  0  0

generates a code of length 23 over Z4 who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+40x^10+124x^12+242x^14+436x^16+1012x^18+2440x^20+3942x^22+3862x^24+2368x^26+1052x^28+478x^30+243x^32+100x^34+32x^36+10x^38+2x^40

The gray image is a code over GF(2) with n=46, k=14 and d=10.
This code was found by Heurico 1.16 in 2.67 seconds.