The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  X  1  1  X  1  1  X  1  1  X  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0 2X  X  X 2X  X  0  X  X 2X  0 2X  X  X  0  X 2X  X  X  0  X  0  X 2X  0
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  0 2X  0 2X 2X 2X  X 2X  X  0  X  X 2X 2X  0 2X  0 2X 2X  X  X 2X  X  0  X  0
 0  0  0  X  0  0  0  0  0  0  X  X  X  X 2X 2X  0 2X  0 2X 2X 2X 2X  0  0 2X  X  0 2X 2X  0  0 2X  X 2X  X  X  X  0  0
 0  0  0  0  X  0  0  0  0  X 2X  X 2X  X  0  X  0  0  0  0  X 2X  0  X  X  0  X  0  X  X  0 2X  0 2X  0  X 2X  0  X  0
 0  0  0  0  0  X  0  0  0 2X 2X  0  X  X  X  X  X 2X  0  X 2X  0  0  0 2X  X  X  X  X  X  0  X 2X  X  X 2X  0  0  0  0
 0  0  0  0  0  0  X  0  0 2X 2X  X  0 2X 2X 2X  X 2X  X 2X 2X  0 2X 2X  X 2X  0  X  0 2X  X  0  0 2X  X  0 2X 2X 2X  X
 0  0  0  0  0  0  0  X  0 2X 2X 2X  0  0  0 2X 2X 2X  X  X  0  X  X 2X  0  X 2X  0  0  0 2X  0 2X  X  0  X 2X  0  X 2X
 0  0  0  0  0  0  0  0  X 2X  X  X 2X  0  X  X  0  X  X  0 2X 2X 2X  X 2X  0  0  0  X 2X 2X  0 2X  0 2X  0  0  0 2X  0

generates a code of length 40 over Z3[X]/(X^2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+82x^57+344x^60+534x^63+848x^66+54x^68+1202x^69+648x^71+1574x^72+3240x^74+2098x^75+8640x^77+2386x^78+12960x^80+2636x^81+10368x^83+2596x^84+3456x^86+2050x^87+1512x^90+916x^93+466x^96+286x^99+98x^102+32x^105+18x^108+4x^111

The gray image is a linear code over GF(3) with n=120, k=10 and d=57.
This code was found by Heurico 1.16 in 45.4 seconds.