The generator matrix

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

generates a code of length 80 over Z4 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+29x^40+36x^42+157x^44+274x^46+432x^48+658x^50+845x^52+996x^54+1209x^56+1074x^58+955x^60+618x^62+449x^64+10x^65+262x^66+114x^67+131x^68+244x^69+48x^70+502x^71+16x^72+948x^73+2x^74+1600x^75+2228x^77+2558x^79+2550x^81+2146x^83+1660x^85+2x^86+994x^87+22x^88+472x^89+62x^90+252x^91+124x^92+76x^93+249x^94+26x^95+422x^96+4x^97+683x^98+914x^100+1080x^102+1074x^104+1127x^106+884x^108+678x^110+390x^112+265x^114+126x^116+59x^118+12x^120+15x^122+3x^126+1x^134

The gray image is a code over GF(2) with n=160, k=15 and d=40.
This code was found by Heurico 1.16 in 99.5 seconds.