The generator matrix

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

generates a code of length 26 over Z4 who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+150x^12+527x^16+1328x^20+6216x^24+6124x^28+1343x^32+576x^36+104x^40+14x^44+1x^48

The gray image is a code over GF(2) with n=52, k=14 and d=12.
This code was found by Heurico 1.16 in 4.02 seconds.