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

generates a code of length 75 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+182x^69+300x^70+470x^71+368x^72+476x^73+306x^74+402x^75+286x^76+268x^77+237x^78+154x^79+145x^80+148x^81+81x^82+110x^83+38x^84+70x^85+19x^86+16x^87+10x^88+8x^89+1x^90

The gray image is a code over GF(2) with n=300, k=12 and d=138.
This code was found by Heurico 1.16 in 0.856 seconds.