The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+56x^40+52x^42+70x^44+32x^46+23x^48+8x^50+2x^52+8x^56+4x^58

The gray image is a code over GF(2) with n=88, k=8 and d=40.
This code was found by Heurico 1.16 in 0.016 seconds.