The generator matrix

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

generates a code of length 21 over Z4 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+40x^14+50x^15+122x^16+142x^17+148x^18+202x^19+190x^20+230x^21+215x^22+214x^23+161x^24+138x^25+103x^26+46x^27+37x^28+2x^29+5x^30+1x^34+1x^36

The gray image is a code over GF(2) with n=42, k=11 and d=14.
This code was found by Heurico 1.16 in 0.0878 seconds.