The generator matrix

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

generates a code of length 75 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+37x^62+109x^64+20x^65+210x^66+308x^67+352x^68+624x^69+427x^70+1504x^71+461x^72+2312x^73+489x^74+2728x^75+474x^76+2432x^77+479x^78+1344x^79+415x^80+708x^81+281x^82+260x^83+166x^84+48x^85+85x^86+43x^88+27x^90+14x^92+12x^94+11x^96+1x^98+2x^100

The gray image is a code over GF(2) with n=300, k=14 and d=124.
This code was found by Heurico 1.16 in 18.3 seconds.