The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+396x^70+400x^71+774x^72+408x^73+657x^74+272x^75+432x^76+192x^77+242x^78+96x^79+110x^80+40x^81+45x^82+21x^84+4x^86+4x^88+1x^92+1x^96

The gray image is a code over GF(2) with n=592, k=12 and d=280.
This code was found by Heurico 1.16 in 1.84 seconds.