The generator matrix

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

generates a code of length 27 over Z4 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+72x^14+275x^16+376x^18+256x^20+572x^22+3412x^24+3552x^26+3016x^28+2804x^30+859x^32+664x^34+304x^36+132x^38+60x^40+16x^42+8x^44+4x^46+1x^48

The gray image is a code over GF(2) with n=54, k=14 and d=14.
This code was found by Heurico 1.16 in 5.84 seconds.