The generator matrix

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

generates a code of length 78 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+134x^73+688x^74+1004x^75+1227x^76+1140x^77+885x^78+700x^79+757x^80+450x^81+421x^82+332x^83+218x^84+100x^85+80x^86+36x^87+4x^88+8x^89+4x^90+1x^92+1x^94+1x^98

The gray image is a code over GF(2) with n=624, k=13 and d=292.
This code was found by Heurico 1.16 in 1.05 seconds.