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

generates a code of length 74 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+67x^68+184x^69+207x^70+412x^71+335x^72+638x^73+614x^74+540x^75+333x^76+320x^77+143x^78+120x^79+50x^80+66x^81+20x^82+16x^83+13x^84+8x^85+8x^86+1x^124

The gray image is a code over GF(2) with n=592, k=12 and d=272.
This code was found by Heurico 1.16 in 0.718 seconds.