The generator matrix

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

generates a code of length 44 over Z4 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+178x^40+40x^42+153x^44+16x^46+61x^48+8x^50+38x^52+16x^56+1x^60

The gray image is a code over GF(2) with n=88, k=9 and d=40.
This code was found by Heurico 1.16 in 2.88 seconds.