The generator matrix

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

generates a code of length 79 over Z4[X]/(X^2+2) 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 1.09 seconds.