The generator matrix

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

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+121x^74+780x^75+884x^76+1122x^77+1039x^78+1200x^79+784x^80+682x^81+448x^82+428x^83+241x^84+226x^85+82x^86+64x^87+40x^88+42x^89+5x^90+1x^94+1x^96+1x^100

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 1.09 seconds.