The generator matrix

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

generates a code of length 54 over Z4 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+150x^44+32x^46+263x^48+132x^50+380x^52+176x^54+371x^56+152x^58+211x^60+16x^62+105x^64+4x^66+42x^68+11x^72+1x^76+1x^80

The gray image is a code over GF(2) with n=108, k=11 and d=44.
This code was found by Heurico 1.16 in 21.1 seconds.