The generator matrix

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

generates a code of length 74 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+158x^68+330x^69+390x^70+422x^71+536x^72+336x^73+332x^74+278x^75+266x^76+226x^77+195x^78+146x^79+135x^80+88x^81+82x^82+46x^83+48x^84+44x^85+33x^86+4x^87

The gray image is a code over GF(2) with n=296, k=12 and d=136.
This code was found by Heurico 1.16 in 0.839 seconds.