The generator matrix

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

generates a code of length 44 over Z4 who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+94x^38+248x^40+168x^42+135x^44+92x^46+104x^48+104x^50+53x^52+14x^54+3x^56+8x^58

The gray image is a code over GF(2) with n=88, k=10 and d=38.
This code was found by Heurico 1.16 in 0.117 seconds.