The generator matrix

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

generates a code of length 75 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+252x^70+208x^71+543x^72+368x^73+535x^74+384x^75+515x^76+384x^77+439x^78+176x^79+204x^80+16x^81+37x^82+15x^84+16x^86+2x^92+1x^118

The gray image is a code over GF(2) with n=600, k=12 and d=280.
This code was found by Heurico 1.16 in 112 seconds.