The generator matrix

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

generates a code of length 74 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+252x^70+52x^71+270x^72+56x^73+770x^74+128x^75+228x^76+8x^77+256x^78+12x^79+12x^80+1x^82+1x^96+1x^114

The gray image is a code over GF(2) with n=592, k=11 and d=280.
This code was found by Heurico 1.16 in 0.297 seconds.