The generator matrix

 1  0  0  1  1  1 2X+2 2X  0  2  1  1  1  1 3X  1  1 3X+2  1  1 3X  1 3X 3X+2  1  X  1  1 3X+2  1  1 X+2  1  1  1 2X+2  1  1  0  0  1  1  1  2  1  1 3X  1  1 3X  1  1  1 3X+2  0 2X  1  1  1  1 2X  1 3X 3X  1  X  1  1  X 2X+2  1  X  1  1
 0  1  0  0  3 2X+3  1 X+2  1  1 2X  0  3  3 3X X+2 X+3  1 X+1  X  1 3X+1  2  1 3X+1  1 X+2 3X  X  0  1  1  1  2 X+2  1 3X+3 3X  1 2X 3X+3  2 2X+3  1  1 3X+3  2 2X+3 X+3  1  2 2X 2X+2  1  1 2X+2  X  2 3X+2 X+2  1 3X+2  1  1 2X+1  1  X  3 2X+2  1  X  1 3X+1  0
 0  0  1 X+1 X+3  2 X+3  1 3X+2  1 X+2  3 2X+1  X  1  3  1 3X+2 3X X+2 X+3 3X+1  1 2X+2  2 2X+1 3X+3 2X  1 2X+1 3X 3X+2 2X+1 3X 3X+1  3  3  2 3X+3  1 3X+1 2X+2  2 2X+1 X+2 3X  1  1 2X+1 2X+1 X+1 3X+2 X+1 2X+3 2X+2  1  X 2X+2  X 2X 2X+1 X+1  0 X+2  0 X+1 X+3 2X  1 2X 2X+1 3X X+1  0
 0  0  0  2  2  0  2 2X+2  2 2X 2X+2 2X 2X 2X+2  0  0  0 2X  2  2  0 2X+2  0  0 2X  2  2  2  2  2  2 2X+2  0  0 2X  0  2 2X+2 2X  2  0  2  2 2X+2 2X 2X  2 2X+2 2X+2 2X 2X+2  0 2X 2X+2  2 2X  0 2X 2X  0  2  2  2  2 2X 2X 2X+2  0 2X 2X+2  0 2X+2  2  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+169x^68+646x^69+1112x^70+1798x^71+1870x^72+2106x^73+1881x^74+1948x^75+1276x^76+1446x^77+933x^78+520x^79+315x^80+186x^81+92x^82+34x^83+15x^84+16x^85+5x^86+2x^87+10x^88+1x^90+2x^91

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 3.37 seconds.