The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+128x^38+185x^40+174x^42+146x^44+122x^46+115x^48+66x^50+52x^52+22x^54+11x^56+2x^60

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 0.0943 seconds.