The generator matrix

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

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+276x^74+930x^76+980x^78+745x^80+818x^82+236x^84+100x^86+4x^88+1x^90+2x^96+2x^100+1x^106

The gray image is a code over GF(2) with n=632, k=12 and d=296.
This code was found by Heurico 1.16 in 1.11 seconds.