The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+96x^68+666x^69+1246x^70+1566x^71+1992x^72+1994x^73+2117x^74+1840x^75+1482x^76+1186x^77+1013x^78+614x^79+250x^80+132x^81+89x^82+56x^83+22x^84+4x^85+5x^86+4x^87+3x^88+2x^89+2x^90+2x^92

The gray image is a code over GF(2) with n=592, k=14 and d=272.
This code was found by Heurico 1.16 in 3.39 seconds.