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  0  2  0  2  0  2  1  0  1  2  1  1  1  0  1  1  0  2  2  0  1  1  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
 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  2  1  0  1  1  0  1  2  1  1  0  0  0  1  1  3  1  1  1  1  2  1  1  3  2  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  1  0  0  0  1  0  1  1  0  2  2  2  3  1  1  3  2  2  2  1  2  1  2  1  2  1  0  1  1  2  1  2  3  2  0  2  2  1  0  3  1  3  1  2  2  1  3  1  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  0  0  1  0  1  0  1  2  1  1  0  3  0  3  2  2  0  0  3  0  3  0  3  3  3  3  1  0  0  2  1  2  0  0  0  3  1  1  2  1  1  3  3  2  0  1  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  1  0  1  1  0  0  0  1  1  1  2  2  0  3  3  2  2  3  3  2  1  3  0  2  3  3  2  1  2  0  0  0  3  0  2  1  0  3  3  3  1  1  1  1  1  1  1  2  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  1  1  1  0  1  1  2  0  1  3  0  2  3  2  0  2  2  1  1  0  1  0  1  1  0  0  0  0  2  1  0  1  0  1  3  0  2  0  3  2  1  2  1  0  1  3  3  2  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  2  0  0  0  2  2  2  0  2  0  2  2  0  2  0  2  0  2  0  0  2  2  2  2  2  2  0  0  2  2  2  0  2  2  2  0  2  0  0  2  2  2  0  0  0  2  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  2  2  2  0  0  0  0  0  2  2  2  2  0  2  0  2  0  2  2  0  0  0  2  0  0  0  0  2  2  2  2  0  0  2  0  2  0  0  0  0  2  2  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  0  2  2  0  0  2  2  2  0  0  2  2  2  0  2  0  0  2  0  0  0  2  0  0  2  2  2  2  0  0  0  0  2  2  0  0  2  2  2  0  0  2  0  0  0  2  0  2  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 77 over Z4 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+8x^40+22x^41+35x^42+56x^43+75x^44+124x^45+178x^46+220x^47+285x^48+348x^49+406x^50+472x^51+469x^52+516x^53+575x^54+600x^55+571x^56+546x^57+536x^58+432x^59+435x^60+334x^61+226x^62+222x^63+214x^64+204x^65+214x^66+228x^67+313x^68+398x^69+491x^70+666x^71+759x^72+956x^73+1051x^74+1210x^75+1332x^76+1294x^77+1310x^78+1196x^79+1074x^80+982x^81+834x^82+638x^83+504x^84+348x^85+291x^86+252x^87+184x^88+218x^89+217x^90+250x^91+231x^92+356x^93+406x^94+412x^95+515x^96+514x^97+603x^98+546x^99+631x^100+568x^101+454x^102+526x^103+406x^104+326x^105+262x^106+212x^107+136x^108+108x^109+82x^110+50x^111+45x^112+28x^113+17x^114+4x^115+1x^116+2x^117+3x^118+2x^120+1x^122+1x^124

The gray image is a code over GF(2) with n=154, k=15 and d=40.
This code was found by Heurico 1.16 in 99.2 seconds.