The generator matrix

 1  0  0  1  1  1  X X+2  1  1  1 X^2+X+2  1 X^2+2  1  1  1  1 X^2+2  X  X X^2+X X+2  1  1  1  X  1  1  2  1  2  1 X^2+X+2  1 X^2+X  1  1  1  2  X  2  1  1  1  1 X^2+X X^2+2  1  1  1  1 X^2  1  0  0  1 X+2  X X^2+X+2 X^2+X+2  1 X^2+X+2  2  1 X^2+X  X  1  1 X^2+2  1 X^2+2  1  1  1 X^2+X+2 X^2+X+2  1
 0  1  0  0 X^2+1 X+1  1  2  0  2 X^2+X+3  1 X^2+X+1  1 X^2+X X+1 X^2+X X^2+3  1 X^2  1 X^2+X+2  1 X^2+X+2  2 X^2+X+3  1 X+3 X+2  1  X  1 X^2+X+1 X^2+2 X^2+3 X+2 X^2+X  3  X X^2+X  1  1 X^2+3 X^2 X+2 X^2+X+1  1  X X^2+X+1 X^2+X+2  0 X^2+X  1 X^2+2  1  1 X^2+3  1  1  1  1  2 X^2+X+2  1 X^2+X  1  1 X^2+X+1 X^2+2 X^2  3  1 X^2  3 X^2+2  1 X^2+2  2
 0  0  1  1  1  0 X^2+1  1  X X^2+X+3  1 X^2+X X^2+X+2  1 X+3 X+1 X^2 X+2 X^2+X+2  1 X^2+X+3  1 X+1  X X^2+X+1 X+1 X+2  X X^2+X X^2 X^2+1 X^2+X+1 X^2+3  1 X^2  1  2 X+3 X+3  1  0 X^2+X+1 X^2+2  0  3 X+2 X^2+X+2  1  0 X+1 X^2+3  2 X^2+2  2 X^2+X+3 X^2+1  0  1 X^2 X^2+X+1 X^2 X+2  1 X+2  1 X^2+3 X^2+X+3 X^2+3  X  1 X^2+3 X^2  X  0 X^2+X+1 X^2+X+2  1  0
 0  0  0  X X+2  2 X+2 X+2 X+2  X X^2+2  X X+2 X^2+2 X^2+2 X^2+X X^2 X^2+X+2  X  2 X^2+2 X^2+X X^2+X+2  X  2 X^2  0 X^2  0 X^2+X+2 X^2+2 X^2+2  X X^2+X+2  X  2  X  0  X X^2+2  0  X X^2+X  X X+2  2 X^2+X+2 X^2+X+2 X^2+X  0 X^2+X+2 X^2+X X+2 X^2 X^2+X+2 X^2+X+2 X^2+2 X^2 X^2+X X+2 X^2 X^2  X  0  2  X  0 X^2+X+2  X  X X+2 X^2+2 X^2+2  2 X^2 X+2  0 X^2

generates a code of length 78 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+100x^71+765x^72+1402x^73+2175x^74+2838x^75+3453x^76+4026x^77+4019x^78+3754x^79+3388x^80+2636x^81+1786x^82+1100x^83+660x^84+290x^85+161x^86+90x^87+76x^88+10x^89+26x^90+6x^91+1x^92+4x^93+1x^98

The gray image is a code over GF(2) with n=624, k=15 and d=284.
This code was found by Heurico 1.16 in 12.2 seconds.