The generator matrix

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

generates a code of length 89 over Z4 who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+112x^80+256x^82+278x^84+280x^86+238x^88+196x^90+178x^92+130x^94+121x^96+92x^98+60x^100+48x^102+16x^104+16x^106+20x^108+6x^110

The gray image is a code over GF(2) with n=178, k=11 and d=80.
This code was found by Heurico 1.16 in 0.898 seconds.