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

generates a code of length 73 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+116x^67+529x^68+1320x^69+1542x^70+1932x^71+1979x^72+2550x^73+1581x^74+1652x^75+984x^76+1028x^77+576x^78+292x^79+160x^80+34x^81+40x^82+20x^83+9x^84+12x^85+10x^86+4x^87+10x^88+3x^90

The gray image is a code over GF(2) with n=584, k=14 and d=268.
This code was found by Heurico 1.16 in 3.37 seconds.