The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+39x^40+48x^41+30x^42+16x^44+64x^45+16x^46+3x^48+16x^49+12x^50+5x^56+6x^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 0.0174 seconds.