The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+165x^38+87x^40+274x^42+76x^44+187x^46+63x^48+104x^50+20x^52+31x^54+9x^56+6x^58+1x^62

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 13.3 seconds.