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

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

Homogenous weight enumerator: w(x)=1x^0+58x^38+71x^40+80x^41+160x^45+47x^46+43x^48+16x^49+22x^54+13x^56+1x^78

The gray image is a code over GF(2) with n=88, k=9 and d=38.
This code was found by Heurico 1.16 in 92.3 seconds.