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

generates a code of length 79 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+128x^73+114x^74+274x^75+265x^76+434x^77+553x^78+712x^79+527x^80+428x^81+228x^82+162x^83+54x^84+104x^85+20x^86+30x^87+10x^88+20x^89+12x^90+4x^91+6x^92+6x^93+2x^95+1x^100+1x^134

The gray image is a code over GF(2) with n=632, k=12 and d=292.
This code was found by Heurico 1.16 in 1.14 seconds.