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

generates a code of length 79 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+168x^74+692x^75+952x^76+1198x^77+999x^78+1192x^79+680x^80+724x^81+352x^82+420x^83+289x^84+270x^85+163x^86+36x^87+28x^88+8x^89+13x^90+4x^91+1x^92+1x^98+1x^104

The gray image is a code over GF(2) with n=632, k=13 and d=296.
This code was found by Heurico 1.16 in 1.02 seconds.